Time-Series Forecasting with Prophet¶

April 2024, Department of Transportation

Description of Session: Want to predict the future? Now you can in just a few clicks! In this session, participants will learn about prophet, a forecasting package built by Facebook developers to make building time-series predictive models incredibly simple. Participants of this session will learn more about the package, the ins and outs of its core features, and get to see it in action to predict rat-related 311 requests at the city level. Attendees will walk away with a step-by-step example of how to use the package and may have some time exploring how to use it for themselves using their own data.

Speaker: Claire Boyd, MSc Candidate in Computational Analysis and Public Policy, University of Chicago

Motivation¶

What is Time Series Analysis or Forecasting?

A time series data is a series of data points or observations recorded at different or regular time intervals. In general, a time series is a sequence of data points taken at equally spaced time intervals. The frequency of recorded data points may be hourly, daily, weekly, monthly, quarterly or annually.

Time series forecasting is a technique used in statistics and machine learning to make predictions about future values based on historical data points that are ordered in time. In a time series, each data point represents a measurement or observation taken at a specific time or over a specific time interval.

A time series analysis encompasses statistical methods for analyzing time series data. These methods enable us to extract meaningful statistics, patterns and other characteristics of the data. So, time series analysis involves understanding inherent aspects of the time series data so that we can create meaningful and accurate forecasts.

Why is it helpful?

Time series analysis is very useful because of how few inputs we need in order to create accurate predictions. In order to create powerful time series models, all we need are two variables - a time stamp and the variable we want to analyze.

Time series analysis can allow us to make more sophisticated predictions about what will happen next. Instead of just knowing that A/C usage will go up in the summer and down in the winter, we can make more sophisticated predictions of what will happen given years of historical trends and better account for contextualize recent fluctations.

General examples:

  • Energy consumption in a neighborhood
  • Purchasing raincoats
  • Web traffic to social media sites

Question for AnEx Members: What are some other NYC-specific examples where time series might be helpful?

How does time series forecasting work?

The goal of time series forecasting is to break down historical data into multiple parts, capturing each component separately in order to mimic the variation of the model.

The original time series is often split into 3 component series:

  • Seasonal: Patterns that repeat with a fixed period of time. For example, a website might receive more visits during weekends; this would produce data with a seasonality of 7 days.
  • Trend: The underlying trend of the metrics. A website increasing in popularity should show a general trend that goes up.
  • Random: Also call “noise”, “irregular” or “remainder,” this is the residuals of the original time series after the seasonal and trend series are removed.

Components of Time Series

How is this typically done?

In short, there are a lot of different statistical or machine learning approaches to separating out our historical data into seasonal components, trend components, and the randomness we want to be left with.

However, it quickly becomes very technical to parse out what the right approach is for your data, asking questions like:

  • Is your data stationary?
  • Does your data exhibit one seasonal trend (think: weekly fluctuations) or multiple seasonal trends (think: weekly, monthly, and yearly)?
  • Does your data's seasonal trends grow with time (aka the effect of the seasonality increases with time)?
  • Are there lags in your data, or are there relationships between your data at specified measurement points? Where are lags statistically significant?

Time Series Model Options

The better you get at time series, the more these choices have meaning and you can make better predictions, but what if you don't have the time to understand these distinctions? How can you build a good time series model without knowing all of this?

Enter, prophet.

What is Prophet?¶

Prophet is an open-source forecasting tool developed by Facebook's Core Data Science team. It is designed for forecasting time series data that exhibits various patterns such as trends, seasonality, and holidays (like we discussed above).

The idea of prophet is that most data practitioners are not experts in time series techniques, so the folks at Facebook have designed a way for you to forecast without needing to get into the nitty gritty of model selection and specification.

Basically, it helps understand your data, choose a model that will best fit your data, and then make predictions based on the model it helps you select.

Here are some key features and characteristics of Prophet (available in python and R):

  • Automatic Handling of Multiple Seasonalities: Prophet can handle time series data with multiple seasonal patterns, which is a common scenario in many real-world applications.

  • Flexibility in Handling Holidays and Special Events: It allows you to include information about holidays and other special events that can impact the time series. This helps in modeling irregularities in the data.

  • Robustness to Missing Data and Outliers: Prophet is designed to handle missing data and outliers in a robust manner. It uses a piecewise linear model to fit the data, which is less sensitive to extreme values.

  • Intuitive Parameter Tuning: Prophet provides a simple and intuitive interface for adjusting hyperparameters. This makes it accessible to users with varying levels of expertise in time series forecasting.

  • Built-in Visualization Tools: Prophet comes with built-in functions for visualizing the forecast and its components, which aids in model interpretation and validation.

Documentation here: https://facebook.github.io/prophet/

Motivating Example: AirPassengers¶

To help us orient around how prophet works, let's choose a simple example with a classic machine learning data set AirPassengers. Here is a quick overview of what the dataset contains.

  • Name: Monthly Airline Passenger Numbers 1949-1960
  • Description: The classic Box & Jenkins airline data. Monthly totals of international airline passengers, 1949 to 1960.
  • Format: A monthly time series, in thousands.
  • Source: Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1976) Time Series Analysis, Forecasting and Control. Third Edition. Holden-Day. Series G.

The raw data for this dataset is available on my github repository and will be read in directly below.

Before we get started, let's make sure that we have pandas available and import it to this jupyter notebook.

In [25]:
pip install pandas
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You should consider upgrading via the 'pip install --upgrade pip' command.
Note: you may need to restart the kernel to use updated packages.
In [26]:
import pandas as pd

Great! Now that we have pandas, let's import our AirPassenger data and take a look at the dataframe and plot.

In [27]:
#url of practice dataset on github, and read in as pandas DataFrame
#url = "https://raw.githubusercontent.com/claireboyd/anex_session/main/AirPassengers.csv"
#airpassengers = pd.read_csv(url, sep=",")
airpassengers = pd.read_csv("AirPassengers.csv", sep=",")


# date object manipulation
airpassengers['date'] = pd.to_datetime(airpassengers['date'])
airpassengers
Out[27]:
date value
0 1949-01-01 112
1 1949-02-01 118
2 1949-03-01 132
3 1949-04-01 129
4 1949-05-01 121
... ... ...
139 1960-08-01 606
140 1960-09-01 508
141 1960-10-01 461
142 1960-11-01 390
143 1960-12-01 432

144 rows × 2 columns

Perfect - we have our data. Now let's plot it.

Question for AnEx Participants: What can we notice about this plot? What components do we think are present in this data?

In [28]:
# #plot using default pandas plot
# airpassengers.plot(x='date',
#                     y='value',
#                     xlabel='Date',
#                     ylabel="Number of Air Passengers (in thousands)",
#                     legend=False,
#                     title='International Airline Travel (1949-1960)',
#                     figsize=(10,3))

Time to bring in prophet. [Note: I am working on a M1 Silicon Chip Mac, using Python 3.8. Here are the set-up instructions I needed: https://blog.quantinsti.com/installing-prophet-library-mac/ but you might have a simplier set up process.]

In [29]:
pip install Cython
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You should consider upgrading via the 'pip install --upgrade pip' command.
Note: you may need to restart the kernel to use updated packages.
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pip install h5py
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pip install pystan==2.19.1.1
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Note: you may need to restart the kernel to use updated packages.
In [32]:
pip install prophet
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In [33]:
from prophet import Prophet

Let's get forecasting.¶

From the documentation, we can see that prophet is particular about the naming convention of our time stamp of our data as well as the variable name of what we want to predict.

Let's re-name our time series "ds" and our output variable "y".

In [34]:
airpassengers_prophet = pd.DataFrame()

airpassengers_prophet["ds"] = airpassengers["date"]
airpassengers_prophet["y"] = airpassengers["value"]
airpassengers_prophet
Out[34]:
ds y
0 1949-01-01 112
1 1949-02-01 118
2 1949-03-01 132
3 1949-04-01 129
4 1949-05-01 121
... ... ...
139 1960-08-01 606
140 1960-09-01 508
141 1960-10-01 461
142 1960-11-01 390
143 1960-12-01 432

144 rows × 2 columns

Perfect. Now let's create an out of the box model with prophet.

We fit the model by instantiating a new Prophet object. Any settings to the forecasting procedure are passed into the constructor. Then you call its fit method and pass in the historical dataframe. Fitting should take 1-5 seconds.

In [35]:
m = Prophet()
m.fit(airpassengers_prophet)
INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5emqt7ct.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gf64wzuf.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=7141', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5emqt7ct.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gf64wzuf.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelor3skasl/prophet_model-20240112165229.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
16:52:29 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
16:52:29 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
Out[35]:
<prophet.forecaster.Prophet at 0x7fd3f0894130>

Predictions are then made on a dataframe with a column ds containing the dates for which a prediction is to be made. You can get a suitable dataframe that extends into the future a specified number of days using the helper method Prophet.make_future_dataframe. By default it will also include the dates from the history, so we will see the model fit as well.

In [36]:
future = m.make_future_dataframe(periods=365)
future.tail()
Out[36]:
ds
504 1961-11-27
505 1961-11-28
506 1961-11-29
507 1961-11-30
508 1961-12-01

The predict method will assign each row in future a predicted value which it names yhat. If you pass in historical dates, it will provide an in-sample fit. The forecast object here is a new dataframe that includes a column yhat with the forecast, as well as columns for components and uncertainty intervals.

In [37]:
forecast = m.predict(future)
forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()
Out[37]:
ds yhat yhat_lower yhat_upper
504 1961-11-27 500.086523 470.433270 528.962828
505 1961-11-28 498.471109 470.498924 524.248745
506 1961-11-29 496.117793 465.701716 525.465521
507 1961-11-30 493.067593 463.768729 521.380224
508 1961-12-01 489.379720 461.055806 516.806422

You can plot the forecast by calling the Prophet.plot method and passing in your forecast dataframe.

In [38]:
fig1 = m.plot(forecast)

Voila! We are forecasting future air passenger visits based on our original dataset!

Let's take a look at how prophet is doing this by examining the "components" of the model.

In [39]:
fig2 = m.plot_components(forecast)

What if we wanted to change the model a bit? How would we customize it?¶

We can always tell prophet what we know about the data to get better estimates. Let's take a look at the defaults and can evaluate if they apply in each circumstance.

In [40]:
help(Prophet)
Help on class Prophet in module prophet.forecaster:

class Prophet(builtins.object)
 |  Prophet(growth='linear', changepoints=None, n_changepoints=25, changepoint_range=0.8, yearly_seasonality='auto', weekly_seasonality='auto', daily_seasonality='auto', holidays=None, seasonality_mode='additive', seasonality_prior_scale=10.0, holidays_prior_scale=10.0, changepoint_prior_scale=0.05, mcmc_samples=0, interval_width=0.8, uncertainty_samples=1000, stan_backend=None)
 |  
 |  Prophet forecaster.
 |  
 |  Parameters
 |  ----------
 |  growth: String 'linear', 'logistic' or 'flat' to specify a linear, logistic or
 |      flat trend.
 |  changepoints: List of dates at which to include potential changepoints. If
 |      not specified, potential changepoints are selected automatically.
 |  n_changepoints: Number of potential changepoints to include. Not used
 |      if input `changepoints` is supplied. If `changepoints` is not supplied,
 |      then n_changepoints potential changepoints are selected uniformly from
 |      the first `changepoint_range` proportion of the history.
 |  changepoint_range: Proportion of history in which trend changepoints will
 |      be estimated. Defaults to 0.8 for the first 80%. Not used if
 |      `changepoints` is specified.
 |  yearly_seasonality: Fit yearly seasonality.
 |      Can be 'auto', True, False, or a number of Fourier terms to generate.
 |  weekly_seasonality: Fit weekly seasonality.
 |      Can be 'auto', True, False, or a number of Fourier terms to generate.
 |  daily_seasonality: Fit daily seasonality.
 |      Can be 'auto', True, False, or a number of Fourier terms to generate.
 |  holidays: pd.DataFrame with columns holiday (string) and ds (date type)
 |      and optionally columns lower_window and upper_window which specify a
 |      range of days around the date to be included as holidays.
 |      lower_window=-2 will include 2 days prior to the date as holidays. Also
 |      optionally can have a column prior_scale specifying the prior scale for
 |      that holiday.
 |  seasonality_mode: 'additive' (default) or 'multiplicative'.
 |  seasonality_prior_scale: Parameter modulating the strength of the
 |      seasonality model. Larger values allow the model to fit larger seasonal
 |      fluctuations, smaller values dampen the seasonality. Can be specified
 |      for individual seasonalities using add_seasonality.
 |  holidays_prior_scale: Parameter modulating the strength of the holiday
 |      components model, unless overridden in the holidays input.
 |  changepoint_prior_scale: Parameter modulating the flexibility of the
 |      automatic changepoint selection. Large values will allow many
 |      changepoints, small values will allow few changepoints.
 |  mcmc_samples: Integer, if greater than 0, will do full Bayesian inference
 |      with the specified number of MCMC samples. If 0, will do MAP
 |      estimation.
 |  interval_width: Float, width of the uncertainty intervals provided
 |      for the forecast. If mcmc_samples=0, this will be only the uncertainty
 |      in the trend using the MAP estimate of the extrapolated generative
 |      model. If mcmc.samples>0, this will be integrated over all model
 |      parameters, which will include uncertainty in seasonality.
 |  uncertainty_samples: Number of simulated draws used to estimate
 |      uncertainty intervals. Settings this value to 0 or False will disable
 |      uncertainty estimation and speed up the calculation.
 |  stan_backend: str as defined in StanBackendEnum default: None - will try to
 |      iterate over all available backends and find the working one
 |  
 |  Methods defined here:
 |  
 |  __init__(self, growth='linear', changepoints=None, n_changepoints=25, changepoint_range=0.8, yearly_seasonality='auto', weekly_seasonality='auto', daily_seasonality='auto', holidays=None, seasonality_mode='additive', seasonality_prior_scale=10.0, holidays_prior_scale=10.0, changepoint_prior_scale=0.05, mcmc_samples=0, interval_width=0.8, uncertainty_samples=1000, stan_backend=None)
 |      Initialize self.  See help(type(self)) for accurate signature.
 |  
 |  add_country_holidays(self, country_name)
 |      Add in built-in holidays for the specified country.
 |      
 |      These holidays will be included in addition to any specified on model
 |      initialization.
 |      
 |      Holidays will be calculated for arbitrary date ranges in the history
 |      and future. See the online documentation for the list of countries with
 |      built-in holidays.
 |      
 |      Built-in country holidays can only be set for a single country.
 |      
 |      Parameters
 |      ----------
 |      country_name: Name of the country, like 'UnitedStates' or 'US'
 |      
 |      Returns
 |      -------
 |      The prophet object.
 |  
 |  add_group_component(self, components, name, group)
 |      Adds a component with given name that contains all of the components
 |      in group.
 |      
 |      Parameters
 |      ----------
 |      components: Dataframe with components.
 |      name: Name of new group component.
 |      group: List of components that form the group.
 |      
 |      Returns
 |      -------
 |      Dataframe with components.
 |  
 |  add_regressor(self, name, prior_scale=None, standardize='auto', mode=None)
 |      Add an additional regressor to be used for fitting and predicting.
 |      
 |      The dataframe passed to `fit` and `predict` will have a column with the
 |      specified name to be used as a regressor. When standardize='auto', the
 |      regressor will be standardized unless it is binary. The regression
 |      coefficient is given a prior with the specified scale parameter.
 |      Decreasing the prior scale will add additional regularization. If no
 |      prior scale is provided, self.holidays_prior_scale will be used.
 |      Mode can be specified as either 'additive' or 'multiplicative'. If not
 |      specified, self.seasonality_mode will be used. 'additive' means the
 |      effect of the regressor will be added to the trend, 'multiplicative'
 |      means it will multiply the trend.
 |      
 |      Parameters
 |      ----------
 |      name: string name of the regressor.
 |      prior_scale: optional float scale for the normal prior. If not
 |          provided, self.holidays_prior_scale will be used.
 |      standardize: optional, specify whether this regressor will be
 |          standardized prior to fitting. Can be 'auto' (standardize if not
 |          binary), True, or False.
 |      mode: optional, 'additive' or 'multiplicative'. Defaults to
 |          self.seasonality_mode.
 |      
 |      Returns
 |      -------
 |      The prophet object.
 |  
 |  add_seasonality(self, name, period, fourier_order, prior_scale=None, mode=None, condition_name=None)
 |      Add a seasonal component with specified period, number of Fourier
 |      components, and prior scale.
 |      
 |      Increasing the number of Fourier components allows the seasonality to
 |      change more quickly (at risk of overfitting). Default values for yearly
 |      and weekly seasonalities are 10 and 3 respectively.
 |      
 |      Increasing prior scale will allow this seasonality component more
 |      flexibility, decreasing will dampen it. If not provided, will use the
 |      seasonality_prior_scale provided on Prophet initialization (defaults
 |      to 10).
 |      
 |      Mode can be specified as either 'additive' or 'multiplicative'. If not
 |      specified, self.seasonality_mode will be used (defaults to additive).
 |      Additive means the seasonality will be added to the trend,
 |      multiplicative means it will multiply the trend.
 |      
 |      If condition_name is provided, the dataframe passed to `fit` and
 |      `predict` should have a column with the specified condition_name
 |      containing booleans which decides when to apply seasonality.
 |      
 |      Parameters
 |      ----------
 |      name: string name of the seasonality component.
 |      period: float number of days in one period.
 |      fourier_order: int number of Fourier components to use.
 |      prior_scale: optional float prior scale for this component.
 |      mode: optional 'additive' or 'multiplicative'
 |      condition_name: string name of the seasonality condition.
 |      
 |      Returns
 |      -------
 |      The prophet object.
 |  
 |  construct_holiday_dataframe(self, dates)
 |      Construct a dataframe of holiday dates.
 |      
 |      Will combine self.holidays with the built-in country holidays
 |      corresponding to input dates, if self.country_holidays is set.
 |      
 |      Parameters
 |      ----------
 |      dates: pd.Series containing timestamps used for computing seasonality.
 |      
 |      Returns
 |      -------
 |      dataframe of holiday dates, in holiday dataframe format used in
 |      initialization.
 |  
 |  fit(self, df, **kwargs)
 |      Fit the Prophet model.
 |      
 |      This sets self.params to contain the fitted model parameters. It is a
 |      dictionary parameter names as keys and the following items:
 |          k (Mx1 array): M posterior samples of the initial slope.
 |          m (Mx1 array): The initial intercept.
 |          delta (MxN array): The slope change at each of N changepoints.
 |          beta (MxK matrix): Coefficients for K seasonality features.
 |          sigma_obs (Mx1 array): Noise level.
 |      Note that M=1 if MAP estimation.
 |      
 |      Parameters
 |      ----------
 |      df: pd.DataFrame containing the history. Must have columns ds (date
 |          type) and y, the time series. If self.growth is 'logistic', then
 |          df must also have a column cap that specifies the capacity at
 |          each ds.
 |      kwargs: Additional arguments passed to the optimizing or sampling
 |          functions in Stan.
 |      
 |      Returns
 |      -------
 |      The fitted Prophet object.
 |  
 |  initialize_scales(self, initialize_scales, df)
 |      Initialize model scales.
 |      
 |      Sets model scaling factors using df.
 |      
 |      Parameters
 |      ----------
 |      initialize_scales: Boolean set the scales or not.
 |      df: pd.DataFrame for setting scales.
 |  
 |  make_all_seasonality_features(self, df)
 |      Dataframe with seasonality features.
 |      
 |      Includes seasonality features, holiday features, and added regressors.
 |      
 |      Parameters
 |      ----------
 |      df: pd.DataFrame with dates for computing seasonality features and any
 |          added regressors.
 |      
 |      Returns
 |      -------
 |      pd.DataFrame with regression features.
 |      list of prior scales for each column of the features dataframe.
 |      Dataframe with indicators for which regression components correspond to
 |          which columns.
 |      Dictionary with keys 'additive' and 'multiplicative' listing the
 |          component names for each mode of seasonality.
 |  
 |  make_future_dataframe(self, periods, freq='D', include_history=True)
 |      Simulate the trend using the extrapolated generative model.
 |      
 |      Parameters
 |      ----------
 |      periods: Int number of periods to forecast forward.
 |      freq: Any valid frequency for pd.date_range, such as 'D' or 'M'.
 |      include_history: Boolean to include the historical dates in the data
 |          frame for predictions.
 |      
 |      Returns
 |      -------
 |      pd.Dataframe that extends forward from the end of self.history for the
 |      requested number of periods.
 |  
 |  make_holiday_features(self, dates, holidays)
 |      Construct a dataframe of holiday features.
 |      
 |      Parameters
 |      ----------
 |      dates: pd.Series containing timestamps used for computing seasonality.
 |      holidays: pd.Dataframe containing holidays, as returned by
 |          construct_holiday_dataframe.
 |      
 |      Returns
 |      -------
 |      holiday_features: pd.DataFrame with a column for each holiday.
 |      prior_scale_list: List of prior scales for each holiday column.
 |      holiday_names: List of names of holidays
 |  
 |  parse_seasonality_args(self, name, arg, auto_disable, default_order)
 |      Get number of fourier components for built-in seasonalities.
 |      
 |      Parameters
 |      ----------
 |      name: string name of the seasonality component.
 |      arg: 'auto', True, False, or number of fourier components as provided.
 |      auto_disable: bool if seasonality should be disabled when 'auto'.
 |      default_order: int default fourier order
 |      
 |      Returns
 |      -------
 |      Number of fourier components, or 0 for disabled.
 |  
 |  percentile(self, a, *args, **kwargs)
 |      We rely on np.nanpercentile in the rare instances where there
 |      are a small number of bad samples with MCMC that contain NaNs.
 |      However, since np.nanpercentile is far slower than np.percentile,
 |      we only fall back to it if the array contains NaNs. See
 |      https://github.com/facebook/prophet/issues/1310 for more details.
 |  
 |  plot(self, fcst, ax=None, uncertainty=True, plot_cap=True, xlabel='ds', ylabel='y', figsize=(10, 6), include_legend=False)
 |      Plot the Prophet forecast.
 |      
 |      Parameters
 |      ----------
 |      fcst: pd.DataFrame output of self.predict.
 |      ax: Optional matplotlib axes on which to plot.
 |      uncertainty: Optional boolean to plot uncertainty intervals.
 |      plot_cap: Optional boolean indicating if the capacity should be shown
 |          in the figure, if available.
 |      xlabel: Optional label name on X-axis
 |      ylabel: Optional label name on Y-axis
 |      figsize: Optional tuple width, height in inches.
 |      include_legend: Optional boolean to add legend to the plot.
 |      
 |      Returns
 |      -------
 |      A matplotlib figure.
 |  
 |  plot_components(self, fcst, uncertainty=True, plot_cap=True, weekly_start=0, yearly_start=0, figsize=None)
 |      Plot the Prophet forecast components.
 |      
 |      Will plot whichever are available of: trend, holidays, weekly
 |      seasonality, and yearly seasonality.
 |      
 |      Parameters
 |      ----------
 |      fcst: pd.DataFrame output of self.predict.
 |      uncertainty: Optional boolean to plot uncertainty intervals.
 |      plot_cap: Optional boolean indicating if the capacity should be shown
 |          in the figure, if available.
 |      weekly_start: Optional int specifying the start day of the weekly
 |          seasonality plot. 0 (default) starts the week on Sunday. 1 shifts
 |          by 1 day to Monday, and so on.
 |      yearly_start: Optional int specifying the start day of the yearly
 |          seasonality plot. 0 (default) starts the year on Jan 1. 1 shifts
 |          by 1 day to Jan 2, and so on.
 |      figsize: Optional tuple width, height in inches.
 |      
 |      Returns
 |      -------
 |      A matplotlib figure.
 |  
 |  predict(self, df: pandas.core.frame.DataFrame = None, vectorized: bool = True) -> pandas.core.frame.DataFrame
 |      Predict using the prophet model.
 |      
 |      Parameters
 |      ----------
 |      df: pd.DataFrame with dates for predictions (column ds), and capacity
 |          (column cap) if logistic growth. If not provided, predictions are
 |          made on the history.
 |      vectorized: Whether to use a vectorized method to compute uncertainty intervals. Suggest using
 |          True (the default) for much faster runtimes in most cases,
 |          except when (growth = 'logistic' and mcmc_samples > 0).
 |      
 |      Returns
 |      -------
 |      A pd.DataFrame with the forecast components.
 |  
 |  predict_seasonal_components(self, df)
 |      Predict seasonality components, holidays, and added regressors.
 |      
 |      Parameters
 |      ----------
 |      df: Prediction dataframe.
 |      
 |      Returns
 |      -------
 |      Dataframe with seasonal components.
 |  
 |  predict_trend(self, df)
 |      Predict trend using the prophet model.
 |      
 |      Parameters
 |      ----------
 |      df: Prediction dataframe.
 |      
 |      Returns
 |      -------
 |      Vector with trend on prediction dates.
 |  
 |  predict_uncertainty(self, df: pandas.core.frame.DataFrame, vectorized: bool) -> pandas.core.frame.DataFrame
 |      Prediction intervals for yhat and trend.
 |      
 |      Parameters
 |      ----------
 |      df: Prediction dataframe.
 |      vectorized: Whether to use a vectorized method for generating future draws.
 |      
 |      Returns
 |      -------
 |      Dataframe with uncertainty intervals.
 |  
 |  predictive_samples(self, df: pandas.core.frame.DataFrame, vectorized: bool = True)
 |      Sample from the posterior predictive distribution. Returns samples
 |      for the main estimate yhat, and for the trend component. The shape of
 |      each output will be (nforecast x nsamples), where nforecast is the
 |      number of points being forecasted (the number of rows in the input
 |      dataframe) and nsamples is the number of posterior samples drawn.
 |      This is the argument `uncertainty_samples` in the Prophet constructor,
 |      which defaults to 1000.
 |      
 |      Parameters
 |      ----------
 |      df: Dataframe with dates for predictions (column ds), and capacity
 |          (column cap) if logistic growth.
 |      vectorized: Whether to use a vectorized method to compute possible draws. Suggest using
 |          True (the default) for much faster runtimes in most cases,
 |          except when (growth = 'logistic' and mcmc_samples > 0).
 |      
 |      Returns
 |      -------
 |      Dictionary with keys "trend" and "yhat" containing
 |      posterior predictive samples for that component.
 |  
 |  regressor_column_matrix(self, seasonal_features, modes)
 |      Dataframe indicating which columns of the feature matrix correspond
 |      to which seasonality/regressor components.
 |      
 |      Includes combination components, like 'additive_terms'. These
 |      combination components will be added to the 'modes' input.
 |      
 |      Parameters
 |      ----------
 |      seasonal_features: Constructed seasonal features dataframe
 |      modes: Dictionary with keys 'additive' and 'multiplicative' listing the
 |          component names for each mode of seasonality.
 |      
 |      Returns
 |      -------
 |      component_cols: A binary indicator dataframe with columns seasonal
 |          components and rows columns in seasonal_features. Entry is 1 if
 |          that columns is used in that component.
 |      modes: Updated input with combination components.
 |  
 |  sample_model(self, df, seasonal_features, iteration, s_a, s_m) -> Dict[str, numpy.ndarray]
 |      Simulate observations from the extrapolated generative model.
 |      
 |      Parameters
 |      ----------
 |      df: Prediction dataframe.
 |      seasonal_features: pd.DataFrame of seasonal features.
 |      iteration: Int sampling iteration to use parameters from.
 |      s_a: Indicator vector for additive components
 |      s_m: Indicator vector for multiplicative components
 |      
 |      Returns
 |      -------
 |      Dictionary with `yhat` and `trend`, each like df['t'].
 |  
 |  sample_model_vectorized(self, df: pandas.core.frame.DataFrame, seasonal_features: pandas.core.frame.DataFrame, iteration: int, s_a: numpy.ndarray, s_m: numpy.ndarray, n_samples: int) -> List[Dict[str, numpy.ndarray]]
 |      Simulate observations from the extrapolated generative model. Vectorized version of sample_model().
 |      
 |      Returns
 |      -------
 |      List (length n_samples) of dictionaries with arrays for trend and yhat, each ordered like df['t'].
 |  
 |  sample_posterior_predictive(self, df: pandas.core.frame.DataFrame, vectorized: bool) -> Dict[str, numpy.ndarray]
 |      Prophet posterior predictive samples.
 |      
 |      Parameters
 |      ----------
 |      df: Prediction dataframe.
 |      vectorized: Whether to use a vectorized method to generate future draws.
 |      
 |      Returns
 |      -------
 |      Dictionary with posterior predictive samples for the forecast yhat and
 |      for the trend component.
 |  
 |  sample_predictive_trend(self, df, iteration)
 |      Simulate the trend using the extrapolated generative model.
 |      
 |      Parameters
 |      ----------
 |      df: Prediction dataframe.
 |      iteration: Int sampling iteration to use parameters from.
 |      
 |      Returns
 |      -------
 |      np.array of simulated trend over df['t'].
 |  
 |  sample_predictive_trend_vectorized(self, df: pandas.core.frame.DataFrame, n_samples: int, iteration: int = 0) -> numpy.ndarray
 |      Sample draws of the future trend values. Vectorized version of sample_predictive_trend().
 |      
 |      Returns
 |      -------
 |      Draws of the trend values with shape (n_samples, len(df)). Values are on the scale of the original data.
 |  
 |  set_auto_seasonalities(self)
 |      Set seasonalities that were left on auto.
 |      
 |      Turns on yearly seasonality if there is >=2 years of history.
 |      Turns on weekly seasonality if there is >=2 weeks of history, and the
 |      spacing between dates in the history is <7 days.
 |      Turns on daily seasonality if there is >=2 days of history, and the
 |      spacing between dates in the history is <1 day.
 |  
 |  set_changepoints(self)
 |      Set changepoints
 |      
 |      Sets m$changepoints to the dates of changepoints. Either:
 |      1) The changepoints were passed in explicitly.
 |          A) They are empty.
 |          B) They are not empty, and need validation.
 |      2) We are generating a grid of them.
 |      3) The user prefers no changepoints be used.
 |  
 |  setup_dataframe(self, df, initialize_scales=False)
 |      Prepare dataframe for fitting or predicting.
 |      
 |      Adds a time index and scales y. Creates auxiliary columns 't', 't_ix',
 |      'y_scaled', and 'cap_scaled'. These columns are used during both
 |      fitting and predicting.
 |      
 |      Parameters
 |      ----------
 |      df: pd.DataFrame with columns ds, y, and cap if logistic growth. Any
 |          specified additional regressors must also be present.
 |      initialize_scales: Boolean set scaling factors in self from df.
 |      
 |      Returns
 |      -------
 |      pd.DataFrame prepared for fitting or predicting.
 |  
 |  validate_column_name(self, name, check_holidays=True, check_seasonalities=True, check_regressors=True)
 |      Validates the name of a seasonality, holiday, or regressor.
 |      
 |      Parameters
 |      ----------
 |      name: string
 |      check_holidays: bool check if name already used for holiday
 |      check_seasonalities: bool check if name already used for seasonality
 |      check_regressors: bool check if name already used for regressor
 |  
 |  validate_inputs(self)
 |      Validates the inputs to Prophet.
 |  
 |  ----------------------------------------------------------------------
 |  Class methods defined here:
 |  
 |  make_seasonality_features(dates, period, series_order, prefix) from builtins.type
 |      Data frame with seasonality features.
 |      
 |      Parameters
 |      ----------
 |      cls: Prophet class.
 |      dates: pd.Series containing timestamps.
 |      period: Number of days of the period.
 |      series_order: Number of components.
 |      prefix: Column name prefix.
 |      
 |      Returns
 |      -------
 |      pd.DataFrame with seasonality features.
 |  
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |  
 |  flat_growth_init(df)
 |      Initialize flat growth.
 |      
 |      Provides a strong initialization for flat growth. Sets the growth to 0
 |      and offset parameter as mean of history y_scaled values.
 |      
 |      Parameters
 |      ----------
 |      df: pd.DataFrame with columns ds (date), y_scaled (scaled time series),
 |          and t (scaled time).
 |      
 |      Returns
 |      -------
 |      A tuple (k, m) with the rate (k) and offset (m) of the linear growth
 |      function.
 |  
 |  flat_trend(t, m)
 |      Evaluate the flat trend function.
 |      
 |      Parameters
 |      ----------
 |      t: np.array of times on which the function is evaluated.
 |      m: Float initial offset.
 |      
 |      Returns
 |      -------
 |      Vector y(t).
 |  
 |  fourier_series(dates: pandas.core.series.Series, period: Union[int, float], series_order: int) -> numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]]
 |      Provides Fourier series components with the specified frequency
 |      and order.
 |      
 |      Parameters
 |      ----------
 |      dates: pd.Series containing timestamps.
 |      period: Number of days of the period.
 |      series_order: Number of components.
 |      
 |      Returns
 |      -------
 |      Matrix with seasonality features.
 |  
 |  linear_growth_init(df)
 |      Initialize linear growth.
 |      
 |      Provides a strong initialization for linear growth by calculating the
 |      growth and offset parameters that pass the function through the first
 |      and last points in the time series.
 |      
 |      Parameters
 |      ----------
 |      df: pd.DataFrame with columns ds (date), y_scaled (scaled time series),
 |          and t (scaled time).
 |      
 |      Returns
 |      -------
 |      A tuple (k, m) with the rate (k) and offset (m) of the linear growth
 |      function.
 |  
 |  logistic_growth_init(df)
 |      Initialize logistic growth.
 |      
 |      Provides a strong initialization for logistic growth by calculating the
 |      growth and offset parameters that pass the function through the first
 |      and last points in the time series.
 |      
 |      Parameters
 |      ----------
 |      df: pd.DataFrame with columns ds (date), cap_scaled (scaled capacity),
 |          y_scaled (scaled time series), and t (scaled time).
 |      
 |      Returns
 |      -------
 |      A tuple (k, m) with the rate (k) and offset (m) of the logistic growth
 |      function.
 |  
 |  piecewise_linear(t, deltas, k, m, changepoint_ts)
 |      Evaluate the piecewise linear function.
 |      
 |      Parameters
 |      ----------
 |      t: np.array of times on which the function is evaluated.
 |      deltas: np.array of rate changes at each changepoint.
 |      k: Float initial rate.
 |      m: Float initial offset.
 |      changepoint_ts: np.array of changepoint times.
 |      
 |      Returns
 |      -------
 |      Vector y(t).
 |  
 |  piecewise_logistic(t, cap, deltas, k, m, changepoint_ts)
 |      Evaluate the piecewise logistic function.
 |      
 |      Parameters
 |      ----------
 |      t: np.array of times on which the function is evaluated.
 |      cap: np.array of capacities at each t.
 |      deltas: np.array of rate changes at each changepoint.
 |      k: Float initial rate.
 |      m: Float initial offset.
 |      changepoint_ts: np.array of changepoint times.
 |      
 |      Returns
 |      -------
 |      Vector y(t).
 |  
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |  
 |  __dict__
 |      dictionary for instance variables (if defined)
 |  
 |  __weakref__
 |      list of weak references to the object (if defined)

Now that we know a bit more about what the defaults are we can correct for the small errors that prophet made.

In [41]:
#change periods to months (its monthly data)
future = m.make_future_dataframe(periods=12, freq='M')
future.tail()
Out[41]:
ds
151 1961-07-31
152 1961-08-31
153 1961-09-30
154 1961-10-31
155 1961-11-30
In [42]:
forecast = m.predict(future)
forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()
Out[42]:
ds yhat yhat_lower yhat_upper
151 1961-07-31 576.204198 546.342428 606.545172
152 1961-08-31 530.442367 500.969643 558.249297
153 1961-09-30 493.102059 465.643198 522.353325
154 1961-10-31 463.415994 434.429011 491.393093
155 1961-11-30 493.067593 463.740671 520.364999
In [43]:
fig1 = m.plot(forecast)
In [44]:
forecast
Out[44]:
ds trend yhat_lower yhat_upper trend_lower trend_upper additive_terms additive_terms_lower additive_terms_upper yearly yearly_lower yearly_upper multiplicative_terms multiplicative_terms_lower multiplicative_terms_upper yhat
0 1949-01-01 107.754658 58.877441 114.436324 107.754658 107.754658 -21.277622 -21.277622 -21.277622 -21.277622 -21.277622 -21.277622 0.0 0.0 0.0 86.477036
1 1949-02-01 109.889284 49.662171 109.170693 109.889284 109.889284 -29.901472 -29.901472 -29.901472 -29.901472 -29.901472 -29.901472 0.0 0.0 0.0 79.987813
2 1949-03-01 111.817334 84.303620 139.873106 111.817334 111.817334 -0.423821 -0.423821 -0.423821 -0.423821 -0.423821 -0.423821 0.0 0.0 0.0 111.393513
3 1949-04-01 113.951960 81.025902 138.605124 113.951960 113.951960 -4.841700 -4.841700 -4.841700 -4.841700 -4.841700 -4.841700 0.0 0.0 0.0 109.110261
4 1949-05-01 116.017728 83.033936 140.798062 116.017728 116.017728 -3.571278 -3.571278 -3.571278 -3.571278 -3.571278 -3.571278 0.0 0.0 0.0 112.446450
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
151 1961-07-31 509.221190 546.342428 606.545172 508.929793 509.546618 66.983007 66.983007 66.983007 66.983007 66.983007 66.983007 0.0 0.0 0.0 576.204198
152 1961-08-31 512.355507 500.969643 558.249297 511.997567 512.747079 18.086859 18.086859 18.086859 18.086859 18.086859 18.086859 0.0 0.0 0.0 530.442367
153 1961-09-30 515.388717 465.643198 522.353325 514.983519 515.835081 -22.286659 -22.286659 -22.286659 -22.286659 -22.286659 -22.286659 0.0 0.0 0.0 493.102059
154 1961-10-31 518.523034 434.429011 491.393093 518.047346 519.033649 -55.107040 -55.107040 -55.107040 -55.107040 -55.107040 -55.107040 0.0 0.0 0.0 463.415994
155 1961-11-30 521.556244 463.740671 520.364999 521.002151 522.147003 -28.488651 -28.488651 -28.488651 -28.488651 -28.488651 -28.488651 0.0 0.0 0.0 493.067593

156 rows × 16 columns

Another Example: Time Series Modeling for Rat-related 311 Requests¶

To inform data-driven rodent mitigation, we can use historic data to give us a better picture of how many rat-related 311 requests we should expect given seasonal trends and compare those predictions to the observed values to prioritize different areas of the city for mitigation resources.

The following script uses prophet to create time-series predictive models hypertuned for each geography of interest (the whole city, boroughs, community boards, and rat mitigation zones). In order to build custom models and generate predictions for the PowerBI dashboard, the code below follows the following steps:

  • Set up: Reads in data, does initial data cleaning.
  • Descriptive analysis: Explores data to confirm time-series analysis is the right approach.
  • Model development: Tests different model parameters, using a grid search to choose the parameters that have the best model performance (using two specific metrics).
  • Data Export for PowerBI: Generates predictions for custom models at all geographies, and saves csvs to sharepoint folder.

Set-up¶

Read-in relevant data¶

Use NYC Open Data Portal to source all rat-related 311 requests that trigger building inspections. This includes all requests that fall under the following complaint types:

  • School Maintenance
  • Food Establishment
  • Rodent
  • Maintenance or Facility
  • Dead Animal
  • Unsanitary Condition

Because not all requests under these types are rat-related, we can subset based on specific descriptors when reading in the data using a specific query.

In [45]:
pip install sodapy
Requirement already satisfied: sodapy in /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages (2.2.0)
Requirement already satisfied: requests>=2.28.1 in /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages (from sodapy) (2.31.0)
Requirement already satisfied: certifi>=2017.4.17 in /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages (from requests>=2.28.1->sodapy) (2023.5.7)
Requirement already satisfied: urllib3<3,>=1.21.1 in /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages (from requests>=2.28.1->sodapy) (2.0.3)
Requirement already satisfied: idna<4,>=2.5 in /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages (from requests>=2.28.1->sodapy) (3.4)
Requirement already satisfied: charset-normalizer<4,>=2 in /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages (from requests>=2.28.1->sodapy) (3.2.0)
WARNING: You are using pip version 19.2.3, however version 23.3.2 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.
Note: you may need to restart the kernel to use updated packages.
In [46]:
import pandas as pd
import numpy as np
from sodapy import Socrata
import input.helpers as helpers

Use function in helpers.py to get rat-related requests and show the number of observations of the resulting dataframe.

In [47]:
df_raw = helpers.get_rat_requests(dataset_id="erm2-nwe9")

# show (observations, variables) in the rat complaints dataframe
df_raw.shape
WARNING:root:Requests made without an app_token will be subject to strict throttling limits.
Out[47]:
(744326, 43)
In [48]:
df_raw.head()
Out[48]:
unique_key created_date agency agency_name complaint_type descriptor location_type incident_zip incident_address street_name ... bridge_highway_direction road_ramp bridge_highway_segment due_date facility_type created_date_dt date week month year
0 59985799 2024-01-11T01:20:24.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting 3+ Family Apt. Building 11203 87 EAST 53 STREET EAST 53 STREET ... NaN NaN NaN NaN NaN 2024-01-11 01:20:24 2024-01-11 2 1 2024
1 59981363 2024-01-11T01:17:27.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting 3+ Family Apt. Building 11221 467 MONROE STREET MONROE STREET ... NaN NaN NaN NaN NaN 2024-01-11 01:17:27 2024-01-11 2 1 2024
2 59988832 2024-01-11T00:31:56.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting Commercial Building 11361 42-41 201 STREET 201 STREET ... NaN NaN NaN NaN NaN 2024-01-11 00:31:56 2024-01-11 2 1 2024
3 59982887 2024-01-11T00:27:19.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting Other (Explain Below) 11375 106-18 QUEENS BOULEVARD QUEENS BOULEVARD ... NaN NaN NaN NaN NaN 2024-01-11 00:27:19 2024-01-11 2 1 2024
4 59984331 2024-01-11T00:23:15.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting 3+ Family Mixed Use Building 11375 69-65 YELLOWSTONE BOULEVARD YELLOWSTONE BOULEVARD ... NaN NaN NaN NaN NaN 2024-01-11 00:23:15 2024-01-11 2 1 2024

5 rows × 43 columns

Check to make sure that all of the rat-related request types are appearing as expected.

In [49]:
df_raw.groupby(['complaint_type', 'descriptor']).agg({'unique_key':'count'})
Out[49]:
unique_key
complaint_type descriptor
Dead Animal Rat or Mouse 2781
Food Establishment Rodents/Insects/Garbage 37723
Maintenance or Facility Rodent Sighting 11641
Rodent Rat Sighting 234593
Signs of Rodents 36944
School Maintenance Rodents/Mice 2977
UNSANITARY CONDITION PESTS 417667

The raw requests dataframe includes categorical variables with different levels of geography that will be helpful later (e.g. community_board and borough) but it does not include our custom 'rat mitigation zones' (RMZs). Using a shapefile saved locally, we can add on an additional categorical variable (rat_mitigation_zone) that will indicate which requests are within RMZs.

In [50]:
pip install geopandas
Requirement already satisfied: geopandas in /Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages (0.13.2)
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WARNING: You are using pip version 19.2.3, however version 23.3.2 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.
Note: you may need to restart the kernel to use updated packages.
In [51]:
import geopandas as gpd

# convert df to gdf and read in rmz shapefile
gdf = gpd.GeoDataFrame(df_raw, geometry = gpd.points_from_xy(df_raw.longitude, df_raw.latitude))
rmzs = gpd.GeoDataFrame.from_file('input/rmz/rmz.shp')

# indicate which requests are within the rmz boundaries
df_with_rmz_labels = gpd.sjoin(gdf, rmzs, how='left', predicate='within')

# Convert revised to df
df = pd.DataFrame(df_with_rmz_labels).rename(columns={'Label':'rat_mitigation_zone',
                                               'NRRType':'is_rmz'})
/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/ipykernel_77679/1129823517.py:8: UserWarning: CRS mismatch between the CRS of left geometries and the CRS of right geometries.
Use `to_crs()` to reproject one of the input geometries to match the CRS of the other.

Left CRS: None
Right CRS: EPSG:4326

  df_with_rmz_labels = gpd.sjoin(gdf, rmzs, how='left', predicate='within')
In [52]:
df.head()
Out[52]:
unique_key created_date agency agency_name complaint_type descriptor location_type incident_zip incident_address street_name ... week month year geometry index_right OBJECTID_1 rat_mitigation_zone is_rmz Shape_Leng Shape_Area
0 59985799 2024-01-11T01:20:24.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting 3+ Family Apt. Building 11203 87 EAST 53 STREET EAST 53 STREET ... 2 1 2024 POINT (-73.92811 40.65800) NaN NaN NaN NaN NaN NaN
1 59981363 2024-01-11T01:17:27.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting 3+ Family Apt. Building 11221 467 MONROE STREET MONROE STREET ... 2 1 2024 POINT (-73.93812 40.68691) NaN NaN NaN NaN NaN NaN
2 59988832 2024-01-11T00:31:56.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting Commercial Building 11361 42-41 201 STREET 201 STREET ... 2 1 2024 POINT (-73.78287 40.75900) NaN NaN NaN NaN NaN NaN
3 59982887 2024-01-11T00:27:19.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting Other (Explain Below) 11375 106-18 QUEENS BOULEVARD QUEENS BOULEVARD ... 2 1 2024 POINT (-73.84724 40.72208) NaN NaN NaN NaN NaN NaN
4 59984331 2024-01-11T00:23:15.000 DOHMH Department of Health and Mental Hygiene Rodent Rat Sighting 3+ Family Mixed Use Building 11375 69-65 YELLOWSTONE BOULEVARD YELLOWSTONE BOULEVARD ... 2 1 2024 POINT (-73.84827 40.72275) NaN NaN NaN NaN NaN NaN

5 rows × 50 columns

Add new col with custom names for RMZs

In [53]:
#change names of RMZs
new_rmz_names = {'Harlem Rat Mitigation Zone':'RMZ Harlem',
                 'Bronx Grand Concourse Zone':'RMZ Bronx',
                 'Brooklyn Bed Stuy and Bushwick':'RMZ Brooklyn',
                 'Manhattan East Village and Chinatown':'RMZ Chinatown/East Village',
                 np.nan: np.nan                 
                }

df['rat_mitigation_zone'] = df['rat_mitigation_zone'].apply(lambda x: new_rmz_names[x])

Descriptive analysis¶

Using the prepared rat-related requests dataframe, we can take a look at some descriptive trends to ensure that a time-series model is the best approach to predict rat-related requests at the daily or weekly level.

In order to streamline this process, I made the following function to aggregate data by a 'level' (week, date or month).

In [54]:
import matplotlib.pyplot as plt
import datetime
In [55]:
def get_aggregates(df, level):
    '''
    Aggregates the input dataframe at the indicated 'level'.
    
    Inputs:
        df (pandas Dataframe): df output from the above data cleaning and set-up.
        level (str): a string to indicate which level to aggregate the number of rat-related 311 requests
            'date' for daily, 'week' for weekly, 'month' for monthly.
    
    Returns: aggregated pandas Dataframe with only 2 columns that are necessary for prophet time series predictions
        ('ds' as the date, and 'y' as the outcome variable of interest)
    '''
    # group by date to get count of 311 rat-related complaints by level
    aggregated_df = df.groupby([level, "year"]).agg({'unique_key':'count',
                                               'created_date':'last'}).reset_index().rename(columns={'unique_key':'y',
                                                                                                       'created_date': 'ds_str'})
    # reformat ds as datetime type
    aggregated_df.loc[:,'ds'] = pd.to_datetime(aggregated_df.loc[:,'ds_str']).dt.round('D')
    aggregated_df = aggregated_df.loc[:,["ds", 'y']].sort_values('ds', ascending=True)
    
    
    # only keep full weeks worth of data - must be less than or equal to the most recent saturday
    today = datetime.date.today()
    idx = (today.weekday() + 1) % 7 # MON = 0, SUN = 6 -> SUN = 0 .. SAT = 6
    last_saturday = today - datetime.timedelta(7+idx-6)

    aggregated_df = aggregated_df.loc[aggregated_df.loc[:,'ds'] <= pd.to_datetime(last_saturday),:]
    
    return aggregated_df

First - we can take a look at daily aggregates of rat-related requests to see if there are year-to-year or seasonal patterns. On a first glance, we can see that there is a big uptick in rat-related requests in the spring of 2014 and strong yearly seasonal trends from 2014-2023. There is a dip in rat-related requests in the spring of 2020 but similar yearly trends seem to pick up by the summer of 2020.

In [56]:
daily = get_aggregates(df, level='date')

#plot daily cases
daily.plot(x='ds', 
           y='y',
           xlabel='Date',
           ylabel="Count of Rat-Related 311 Requests",
           legend=False,
           title='Rat-Related 311 Requests (Jan 2010-July 2023) by Day',
           figsize=(10,3))
Out[56]:
<Axes: title={'center': 'Rat-Related 311 Requests (Jan 2010-July 2023) by Day'}, xlabel='Date', ylabel='Count of Rat-Related 311 Requests'>

To give more context around the uptick of rat-related requests in 2014, let's take a look at the annual trends of each type of complaint. The below plot indicates that unsanitary condition requests started to be categorized in 2014 and Dead Animal requests started to be categorized in 2021. This unsanitary condition uptick gives us more clarity that rat-related 311 requests didn't only increase in 2014 due to additional requests but increased due to additional categories of rat-related requests.

In [57]:
# number of complaints by year and by complaint type
yearly = df.groupby(["year", "complaint_type"]).agg({'unique_key':'count'}).reset_index().rename(columns={'unique_key':'count'})
yearly = yearly.pivot(index='year', columns='complaint_type', values='count').reset_index().reindex()

# plot yearly complaints by type
yearly.plot(x='year',
                 title='Annual Volume of 311 Requests by Complaint Type',
                 xlabel='Year',
                 ylabel="Number of Rat-related 311 requests",
                 figsize=(10,3))
Out[57]:
<Axes: title={'center': 'Annual Volume of 311 Requests by Complaint Type'}, xlabel='Year', ylabel='Number of Rat-related 311 requests'>

Similar to the daily trend data, there seem to be strong yearly seasonal trends after 2014.

In [58]:
weekly = get_aggregates(df, level='week')

# plot weekly cases
weekly.plot(x='ds',
           y='y',
           xlabel='Date',
           ylabel="Count of Rat-Related 311 Requests",
           legend=False,
           title='Rat-Related 311 Requests (Jan 2010-July 2023) by Week',
           figsize=(10,3))
Out[58]:
<Axes: title={'center': 'Rat-Related 311 Requests (Jan 2010-July 2023) by Week'}, xlabel='Date', ylabel='Count of Rat-Related 311 Requests'>

Plotting weekly totals by the week of the year (0-52, because python starts counting at 0), we can see that there is a clear curve of yearly cases. Across all years of data, rat-related 311 requests start lower in the beginning of the year, peak in the summer, and then drop off towards the end of the year in colder months. The darker lines depict averages over time-based clusters (2010-2013, 2014-2016, 2017-2019, 2020, 2021-2023).

In [59]:
# agg number of complaints by week, year
weekly_summary = df.groupby(["week", "year"]).agg({'unique_key': 'count'}).reset_index().rename(columns={'unique_key': "count"})
weekly_summary = weekly_summary.pivot(index='week', columns='year', values='count').reset_index().reindex()

# create new cols with averages
weekly_summary['avg_2010_2013'] = weekly_summary[[2010, 2011, 2012, 2013]].mean(axis=1)
weekly_summary['avg_2014_2016'] = weekly_summary[[2014, 2015, 2016]].mean(axis=1)
weekly_summary['avg_2017_2019'] = weekly_summary[[2017, 2018, 2019]].mean(axis=1)
weekly_summary['avg_2021_2023'] = weekly_summary[[2021, 2022, 2023, 2024]].mean(axis=1)
weekly_summary = weekly_summary.drop(['week'], axis=1)

weekly_summary.plot(use_index=False,
                     color={#group - orange
                            'avg_2010_2013': "#ff8112",
                            2009: "#fcc99d",
                            2010: "#fcc99d",
                            2011: "#fcc99d",
                            2012: "#fcc99d",
                            2013: '#fcc99d',
                            #group - green
                            'avg_2014_2016': '#10800e',
                            2014: '#ccf2cb',
                            2015: '#ccf2cb',
                            2016: '#ccf2cb',
                            #group - blue
                            'avg_2017_2019': '#055c9e',
                            2017: '#b8daf5',                         
                            2018: "#b8daf5",
                            2019: "#b8daf5",
                            #red
                            2020: "#ff1212",
                            #group - purple
                            'avg_2021_2023': '#5e1085',
                            2021: '#e2bcf5',
                            2022: '#e2bcf5',
                            2023: '#e2bcf5',
                            2024: '#e2bcf5'
                            },
                     xlabel="Week of the Year",
                     ylabel="Number of Rat-related 311 requests",
                     figsize=(12,6),
                     title="Annual Trends in Rat-related 311 requests"
                     )

plt.xlabel("Week of the Year")
Out[59]:
Text(0.5, 0, 'Week of the Year')
In [60]:
monthly = get_aggregates(df, level='month')

# plot weekly cases
monthly.plot(x='ds',
           y='y',
           xlabel='Date',
           ylabel="Count of Rat-Related 311 Requests",
           legend=False,
           title='Rat-Related 311 Requests (Jan 2010-July 2023) by Month',
           figsize=(10,3))
Out[60]:
<Axes: title={'center': 'Rat-Related 311 Requests (Jan 2010-July 2023) by Month'}, xlabel='Date', ylabel='Count of Rat-Related 311 Requests'>

Subsetting train and test sets¶

Given the descriptive trends above, we need to decide what subset of the data to use to train our time-series model. Given that unsanitary conditions only started to be categorized in the spring of 2014, we can train the model on data after that shift in order to minimize the likelihood that the model will try to model based on that shift. That said, the model will be trained on data from June 2014-2022 and tested on data after June 2022.

The data is available at the daily level, but there are significant weekly trends (e.g. fewer complaints on sat/sun) so we can try modeling two different levels of aggregation (daily and weekly totals).

In [61]:
import datetime

def train_test_split(df,
                     n_months_to_predict=3,
                     train_start=None, 
                     train_end=None, 
                     test_start=None, 
                     test_end=None):
    '''
    Split a dataset into training and testing data based on input dates and level of aggregation.
    
    Inputs:
        df (pandas dataframe)
        train_start (str): in format "YYYY-MM-DD"
        train_end (str): in format "YYYY-MM-DD"
        test_start (str): in format "YYYY-MM-DD"
        test_end (str): in format "YYYY-MM-DD"
    
    Returns:
        df_train (pandas dataframe)
        df_test (pandas dataframe)
    '''
    #set defaults given n_months_to predict
    if test_end is None:
        #offset by one day so that it is complete data
        test_end = datetime.date.today() - pd.DateOffset(days=1) 

    if test_start is None:
        #get n months of data given input n_months
        test_start = test_end - pd.DateOffset(months=n_months_to_predict)

    if train_end is None:
        #offset train end by one day before test start
        train_end = test_start - pd.DateOffset(days=1)
    
    if train_start is None:
        train_start = '2014-06-01'

    for date in [train_start, train_end, test_start, test_end]:
        date = pd.to_datetime(date)
       
    train = df.loc[(df.loc[:,'ds'] >= train_start) & (df.loc[:,'ds'] < train_end),:] 
    test = df.loc[(df.loc[:,'ds'] >= test_start) & (df.loc[:,'ds'] < test_end),:]
    
    return train, test

The below visualizations clarify what data is used to train and test the daily and weekly models.

Daily¶
In [62]:
#use function to get training and test data sets
daily_train, daily_test = train_test_split(df=daily, n_months_to_predict=8)
daily_subset = pd.concat([daily_train, daily_test], axis=0, keys=['train', 'test']).reset_index()

# plot training and testing data
plt.figure(figsize=(10,6))
groups = daily_subset.groupby('level_0')

for name, group in groups:
    plt.plot(group.ds, 
             group.y,
             marker='o', 
             linestyle='-', 
             markersize=1, 
             label=name)

plt.xlabel('Date')
plt.ylabel('Count of Rat-Related 311 Requests')
plt.title('Rat-Related 311 Requests (June 2014-June 2022) - Daily')
plt.legend()
Out[62]:
<matplotlib.legend.Legend at 0x7fd230034be0>
Weekly¶
In [63]:
#use function to get training and test data sets
weekly_train, weekly_test = train_test_split(df=weekly, n_months_to_predict=8)
weekly_subset = pd.concat([weekly_train, weekly_test], axis=0, keys=['train', 'test']).reset_index()

# plot training and testing data
plt.figure(figsize=(10,6))
groups = weekly_subset.groupby('level_0')

for name, group in groups:
    plt.plot(group.ds, 
             group.y,
             marker='o', 
             linestyle='-', 
             markersize=1, 
             label=name)

plt.xlabel('Date')
plt.ylabel('Count of Rat-Related 311 Requests')
plt.title('Rat-Related 311 Requests (June 2014-June 2022) - Weekly')
plt.legend()
Out[63]:
<matplotlib.legend.Legend at 0x7fd1da1c8d00>
Monthly¶
In [64]:
#use function to get training and test data sets
monthly_train, monthly_test = train_test_split(df=monthly, n_months_to_predict=3)
monthly_subset = pd.concat([monthly_train, monthly_test], axis=0, keys=['train', 'test']).reset_index()

# plot training and testing data
plt.figure(figsize=(10,6))
groups = monthly_subset.groupby('level_0')

for name, group in groups:
    plt.plot(group.ds, 
             group.y,
             marker='o', 
             linestyle='-', 
             markersize=1, 
             label=name)

plt.xlabel('Date')
plt.ylabel('Count of Rat-Related 311 Requests')
plt.title('Rat-Related 311 Requests (June 2014-June 2022) - Monthly')
plt.legend()
Out[64]:
<matplotlib.legend.Legend at 0x7fd287ebe1f0>

Model Development¶

Overview of Prophet Model¶

The Prophet model is a time series forecasting tool developed by Facebook's Core Data Science team. It is designed to handle time series data with strong seasonal patterns and holidays. The model incorporates various components, including trend, seasonality (modeled using Fourier series), and holiday effects, providing an easy-to-use and effective solution for forecasting tasks. Prophet models can be tuned with a variety of trend and seasonality/holiday parameters.

In [65]:
import prophet
from prophet import Prophet
import matplotlib.pyplot as plt
import itertools

Assessing Model Fit¶

Before we play around with changing our model parameters, we will define a few measures of model performance to compare models to each other.

  • Coverage of Prediction Intervals: If your Prophet model provides prediction intervals, you can assess how well the intervals capture the actual data. A higher percentage of actual data falling within the prediction intervals indicates better calibration. If we maximize being “within” prediction intervals, we are optimizing the model for the shape of the data and predicting outliers successfully. This puts less weight on individual weekly predictions being accurate, but rather that the most values are within the range we are looking at. Right now, this makes the most sense to be based on what we want to use the model for!

  • Mean Absolute Percentage Error (MAPE): MAPE measures the percentage difference between the actual and predicted values. It provides a relative measure of the forecasting accuracy, making it easier to interpret. MAPE is not sensitive to the scale of the data, making it more appropriate when dealing with datasets with varying scales. One limitation of MAPE is that it can be sensitive to small actual values, as the percentage error can become very large for small denominators. This can result in a larger impact on the overall error for smaller actual values. MAPE values closer to zero indicate better performance. If we prioritize minimizing MAPE, we are selecting the model that minimizes the average percentage of the actual value of rat-related 311 requests the prediction is off by in our test data set. This metric might do worse with smaller geographies because the magnitude of those values are so small so the percentage adjustments would be larger for those differences between the predicted and actual values (think: a small Bronx community district with 5 rat-related requests one week and 20 the next month would likely do poorly and this metric might be high).

As we finetune our model parameters, we are aiming to maximize the coverage of prediction intervals (first priority) and minimize MAPE (second priority).

In [66]:
import numpy as np

def percentage_in_confidence_interval(forecast):
    '''
    Calculates the number of actual values that fall within the predicted confidence interval (80% certainty) 
    
    Input: pandas Dataframe, "forecast" output from prophet model
    Return: dictionary (key is string, value is float) which has percentages of actual values that fall
        within expected range, above expected range, and below the expected range.
    '''
    # create new column in df that categorizes the yhat in relation to y
    forecast.loc[:,'in_conf_int'] = "within expected range"
    forecast.loc[(forecast.loc[:,'y'] > forecast.loc[:,'yhat_upper']), 'in_conf_int'] = "above expected range"
    forecast.loc[(forecast.loc[:,'y'] < forecast.loc[:,'yhat_lower']), 'in_conf_int'] = "below expected range"
    
    # return dictionary of frequencies of each of those values
    return dict((forecast.loc[:,'in_conf_int'].value_counts()/forecast.shape[0])*100)

def mean_absolute_percentage_error(forecast):
    '''
    Calculates the mean absolute percentage error of the forecast.
    
    Inputs: pandas Dataframe, "forecast" output from prophet model
    Return: MAPE as a float
    '''
    y_true, y_pred = np.array(forecast.loc[:,'y']), np.array(forecast.loc[:,'yhat'])
    return (np.mean(np.abs(y_true - y_pred) / y_true) * 100)

Because we'll be making a lot of different models and want to test for their fit, lets make a function that creates a plot of predictions given a model and returns the forecast as a dataframe so that we can calculate MAPE and percent in confidence interval.

In [67]:
def get_forecast(model, train, test, level, plot=True, title_suffix=''):
    '''
    Get the forecast table from prophet, and plot if indicated.
    
    Inputs: 
        model: Prophet model object
        train: pandas Dataframe of train data (includes 'ds','y' - output of train_test_split function)
        test: pandas Dataframe of test data (includes 'ds','y'- output of train_test_split function)
        plot: boolean - defaults to True
        title suffix: string, used when labeling plots for smaller geographies.
    
    Returns: pandas Dataframe of forecast (note: if plot=True, the plot is printed but it is not returned.)
    '''
    #set number of predictions based on the size of the test data
    periods = test.shape[0]
    
    if level == "date":
        freq='D'
    if level == "week":
        freq='W'
    if level == "month":
        freq='M'
    
    # fit model with train data
    model.fit(train)

    # predict 1 year of data
    future = model.make_future_dataframe(periods=periods, include_history=False, freq=freq)
    forecast = model.predict(future)

    # join in 1 year of test data to forecase (actual values)
    test = test.set_index(forecast.index)
    forecast.loc[:,'y'] = test.loc[:,'y']

    if plot == True:
        # plot forecast
        fig1 = model.plot(forecast, figsize=(10,3))
        a = prophet.plot.add_changepoints_to_plot(fig1.gca(), model, forecast)

        plt.scatter(x=test['ds'], y=test['y'], c='red',marker='.')
        plt.xlabel("Year")
        plt.ylabel("Number of Rat-Related 311 Requests")
        
        if title_suffix != '':
            plt.title(level.title()+" Predicted Rat-Related 311 Calls for "+ title_suffix)
        else:
            plt.title(level.title()+" Predicted Rat-Related 311 Calls")
    
    return forecast

Default Models (daily, weekly, monthly)¶

Before we start fine tuning our model parameters, let's look at the model fit with the baseline, out-of-the-box model at the daily, monthly, and weekly levels.

In [68]:
daily_m = Prophet()

daily_forecast = get_forecast(model=daily_m, 
                              train=daily_train, 
                              test=daily_test, 
                              level="date")
INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
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In [69]:
percentage_in_confidence_interval(daily_forecast)
Out[69]:
{'within expected range': 51.867219917012456,
 'below expected range': 28.63070539419087,
 'above expected range': 19.502074688796682}
In [70]:
mean_absolute_percentage_error(daily_forecast)
Out[70]:
25.15669085088939

Let's compare this running the default model on our weekly data.

In [71]:
weekly_m = Prophet()

weekly_forecast = get_forecast(model=weekly_m, 
                               train=weekly_train, 
                               test=weekly_test, 
                               level="week")
INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
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In [72]:
percentage_in_confidence_interval(weekly_forecast)
Out[72]:
{'within expected range': 64.70588235294117,
 'below expected range': 29.411764705882355,
 'above expected range': 5.88235294117647}
In [73]:
mean_absolute_percentage_error(weekly_forecast)
Out[73]:
8.261531957995365
In [74]:
monthly_m = Prophet()

monthly_forecast = get_forecast(model=monthly_m, 
                               train=monthly_train, 
                               test=monthly_test, 
                               level="month")
INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
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DEBUG:cmdstanpy:idx 0
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DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=34831', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/m69l8ukv.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/7kcs9b3a.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelzh_s5tcc/prophet_model-20240112165430.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
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In [75]:
percentage_in_confidence_interval(monthly_forecast)
Out[75]:
{'below expected range': 100.0}
In [76]:
mean_absolute_percentage_error(monthly_forecast)
Out[76]:
76.38131080076454

The goal of creating this predictive model is to give real-time indications of where rat-related 311 requests are outside of expectations, so aggregating at the month level would not give the right level of quick feedback for decision making.

Although the weekly model has a poor model fit with the default model, it's shape seems to be a right for the data and therefore might be a better candidate for parameter fine tuning in order to improve model predictions.

Parameter Tuning¶

Default Model

The default Prophet models above used the following parameters, descriptions below.

init(self, growth='linear', changepoints=None, n_changepoints=25, changepoint_range=0.8, yearly_seasonality='auto', weekly_seasonality='auto', daily_seasonality='auto', holidays=None, seasonality_mode='additive', seasonality_prior_scale=10.0, holidays_prior_scale=10.0, changepoint_prior_scale=0.05, mcmc_samples=0, interval_width=0.8, uncertainty_samples=1000, stan_backend=None)

There are a lot of parameters to unpack (you can explore all of them by uncommenting the code below (help(Prophet)), but let's explore a few that will help control how our model will work.

In [77]:
#help(Prophet)

Changepoints

Changepoints are essentially dates where there was a shift in behavior in the time series data. In many real-world scenarios, time series data can exhibit various structural breaks due to external events, policy changes, or shifts in user behavior (think: COVID and it's impact on reporting 311 requests in March 2020). If these changepoints are not appropriately accounted for, the forecasting model may have a harder time separating the trend line from seasonal patterns and therefore might make unreliable predictions.

Prophet allows for automatic detection of changepoints by considering potential locations in the time series where a change might occur. It then evaluates the impact of each potential changepoint on the overall model performance and selects the most relevant ones to incorporate in the forecasting process.

In order to capture these changepoints appropriately in the model, there are a few parameters that are relevant:

  • changepoint_range (default: 0.8): Proportion of history in which trend changepoints will be estimated. Defaults to 0.8 for the first 80%. Not used if changepoints is specified.
  • changepoint_prior_scale (default: 0.5): Parameter that controls the flexibility of the trend around the changepoints. Higher values make the trend more flexible, allowing it to fit more closely to the data points and potentially capturing more changepoints.

By identifying and including changepoints in the model, Prophet can better adapt to the time series data's inherent non-stationarity and provide more accurate and robust forecasts. However, it's essential to strike a balance when choosing the changepoint_prior_scale parameter to avoid overfitting to noise or detecting too many changepoints.

For our purposes, we can do some tests to explore what changepoint parameters best fit our city-wide weekly model.

Modeling seasonality with fourier series¶

Fourier series is a mathematical technique that can approximate a wide range of periodic functions by combining sine and cosine functions with different frequencies and amplitudes. In the context of Prophet, the Fourier order determines the number of Fourier terms used to model the seasonality component of the time series. Each Fourier term is composed of two components: a sine term and a cosine term. These terms combine to form a wave pattern with a particular frequency. By increasing the Fourier order, you allow the model to capture more complex and higher-frequency seasonality patterns in the data.

As we increase the fourier order (from 1 to 4), we can see below that the line is more sensitive to fluctuations in faster-changing cycles.

Fourier

(credit: Deepti Goyal, Analytics Vidhya)

Choosing the appropriate Fourier order for the relevant data is crucial in the Prophet model, as using too few terms might result in underfitting, leading to the model being unable to capture the full complexity of the seasonality. On the other hand, using too many terms can lead to overfitting, where the model fits noise in the data rather than true patterns.

In order to capture these changepoints appropriately in the model, there are a few parameters that are relevant:

  • yearly_seasonality (default: 'auto'): Fit yearly seasonality. Can be 'auto', True, False, or a number of Fourier terms to generate.
  • weekly_seasonality (default: 'auto'): Fit weekly seasonality. Can be 'auto', True, False, or a number of Fourier terms to generate.
  • daily_seasonality (default: 'auto'): Fit daily seasonality. Can be 'auto', True, False, or a number of Fourier terms to generate.

According to greykite, a time-series forecasting library, typical values are <= 4, up to 12 for daily seasonality, and up to 15 for yearly seasonality. The forecast will not improve (and may get worse) if Fourier order is too high.

The Fourier order k should satisfy k <= (n_levels+1)/2. n_levels is the number of possible values in a cycle. For example, if your input data is at daily frequency:

  • monthly seasonality: n_levels=31 days in a month.

  • weekly seasonality: n_levels=7 days in a week.

  • daily seasonality: n_levels=1 hours in a day.

Therefore if we use weekly data, then the following would apply:

  • yearly seasonality: n_levels=52 weeks in a year. (52 + 1)/2 = 26.5 max

  • quarterly seasonality: n_levels=13 weeks in a quarter. (13 + 1)/2 = 7 max

  • monthly seasonality: n_levels=4 weeks in a month. (4 + 1)/2 = 2.5 max

For our purposes, we can do some tests to explore what fourier parameters to use to fine tune our models.

In [78]:
# set options of parameters to test
params = {
    # changepoint parameters
    'changepoint_range': [0.8, 0.85, 0.9],
    'changepoint_prior_scale': [0.5, 0.6, 0.7],
    # seasonality parameters
    'm_fourier': [False, 2, 3],
    'q_fourier': [False, 4, 5, 6, 7],
    'y_fourier': [False, 10, 11, 12]
}

In order to see what parameters work the best, let's run all combinations of these parameters and see which models perform best. First, let's make sure that the amount of model runs is reasonable to test (less than 600 or so is fine and should only take a minute or so).

In [79]:
# Generate all combinations of parameters
all_params = [dict(zip(params.keys(), v)) for v in itertools.product(*params.values())]
len(all_params)
Out[79]:
540

Because we will likely need to do these for smaller geographies, we can functionalize this optimization process (called grid searching), returning the parameters that optimize the percentage of actual values within the confidence interval, and then the mean_absolute_percentage_error if there is a tie for "within CI".

In [80]:
def build_model(params):
    '''
    Builds a model given a dictionary of parameters:
    
    Inputs: params (dict), keys are names of Prophet() parameters, values are the values of the parameters
    Returns: Prophet model object    
    '''
    # set model with passed in parameters
    m = Prophet(changepoint_range=params['changepoint_range'],
                changepoint_prior_scale=params['changepoint_prior_scale'],

                # defaults across all models
                daily_seasonality=False,
                weekly_seasonality=False)

    # add seasonality
    if params['m_fourier'] != False:
        m.add_seasonality(name='monthly', period=30.5, fourier_order=int(params['m_fourier']))
    if params['q_fourier'] != False:
        m.add_seasonality(name='quarterly', period=365.25/4, fourier_order=int(params['q_fourier']))
    if params['y_fourier'] != False:
        m.add_seasonality(name='yearly', period=365.25, fourier_order=int(params['y_fourier']))

    return m
In [81]:
from joblib import Parallel, delayed

def evaluate_model(params, level, train, test):
    '''
    Generates dictionary of performance metrics for a model, including the params used to generate the model.
    
    Inputs: 
        params: dictionary of model parameters to use
        level: string, either 'date', 'week', or 'month'
        train: pandas Dataframe of train data (includes 'ds','y' - output of train_test_split function)
        test: pandas Dataframe of test data (includes 'ds','y'- output of train_test_split function)
    
    Returns: dictionary with metrics to evaluate model and params used to generate the model.
    '''
    # set model with passed in parameters
    m = build_model(params=params)
        
    # get forecast
    forecast = get_forecast(model=m, 
                            train=train, 
                            test=test, 
                            level=level,
                            plot=False)

    # create dictionary to track the performance metrics for each model run and populate dict with perfomance stats
    model_performance = {}
    
    # add all params to dictionary
    for key, value in params.items():
        model_performance[key] = value
    
    # add MAPE and percent in CI to dictionary
    model_performance['mean_absolute_percentage_error'] = mean_absolute_percentage_error(forecast)

    for key, value in percentage_in_confidence_interval(forecast).items():
        model_performance[key] = value

    return model_performance
In [82]:
from datetime import date

def grid_search(df, all_params, level, return_best_model_only, n_months_to_predict):
    '''
    Tries all possible model options to find the best params to optimize the model based on highest percentage within
    expected range and lowest MAPE.
    
    Inputs:
        df: pandas dataframe (before spliting for train, test - all data of interest)
        all params: list of dictionaries that have all possible options of params to try
        return_best_model_only: boolean, True if you want only the best params available, 
            False if you want results for all the models generated
        n_months_to_predict: integer for the number of months of data you want to predict
    
    Returns: df of ranked models or dictionary of the params of the best model only 
        (depending on the boolean value for 'return_best_model_only')  
    '''

    aggregated_df = get_aggregates(df, level)

    train, test = train_test_split(df=aggregated_df, 
                                   n_months_to_predict=n_months_to_predict)

    #if not enough data in either set for meaningful predictions
    if train.shape[0] < 5 or test.shape[0] == 0:
        return {}
    
    results = Parallel(n_jobs=-1)(delayed(evaluate_model)(params,level,train,test) for params in all_params)

    ranked_models = pd.DataFrame.from_records(results).sort_values(['within expected range', 'mean_absolute_percentage_error'],
                                                               ascending=[False, True])
    
    if return_best_model_only is True:
        return ranked_models.iloc[0]
    else:
        return ranked_models
In [83]:
ranked_models = grid_search(df=df, 
                            all_params=all_params,
                            level='week', 
                            return_best_model_only=False,
                            n_months_to_predict=3)
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In [84]:
ranked_models.head(10)
Out[84]:
changepoint_range changepoint_prior_scale m_fourier q_fourier y_fourier mean_absolute_percentage_error within expected range below expected range
116 0.8 0.6 3 7 False 8.240523 75.0 25.0
117 0.8 0.6 3 7 10 8.240523 75.0 25.0
96 0.8 0.6 2 7 False 8.243071 75.0 25.0
176 0.8 0.7 3 7 False 8.263690 75.0 25.0
177 0.8 0.7 3 7 10 8.263690 75.0 25.0
57 0.8 0.5 3 7 10 8.270247 75.0 25.0
32 0.8 0.5 2 6 False 8.273315 75.0 25.0
33 0.8 0.5 2 6 10 8.273315 75.0 25.0
156 0.8 0.7 2 7 False 8.277742 75.0 25.0
36 0.8 0.5 2 7 False 8.306925 75.0 25.0

The above table shows us the top 10 models given the range of parameters tested. The best weekly model is a great improvement from our default model just by changing a few parameters! We went from 1.9% within our prediction confidence interval to over 50%. This shows that Prophet is super sensitive to these parameters.

Modifying test/train split¶

Test to see if changing the dates for the train/test split help improve model fit.

In [85]:
best_city_model = ranked_models.iloc[0].to_dict()
best_city_model
Out[85]:
{'changepoint_range': 0.8,
 'changepoint_prior_scale': 0.6,
 'm_fourier': 3,
 'q_fourier': 7,
 'y_fourier': False,
 'mean_absolute_percentage_error': 8.240522968014972,
 'within expected range': 75.0,
 'below expected range': 25.0}
In [86]:
model_performance_dates = {}
level = 'week'

weekly = get_aggregates(df, level=level)

for n_months in range(12,1,-1):
    # use function to get training and test data sets
    train, test = train_test_split(df=weekly, 
                                   n_months_to_predict=n_months)

    # set model with passed in parameters
    m = build_model(params=best_city_model)
    
    # get forecast
    forecast = get_forecast(model=m, 
                            train=train, 
                            test=test, 
                            level=level,
                            plot=False,
                            title_suffix= str(n_months)+" months")
    
    model = {}
    
    # add MAPE and percent in CI to dictionary
    model['mean_absolute_percentage_error'] = mean_absolute_percentage_error(forecast)

    for key, value in percentage_in_confidence_interval(forecast).items():
        model[key] = value

    # save dictionary to model_performance dictionary
    model_performance_dates[n_months] = model

pd.DataFrame(model_performance_dates).T
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Out[86]:
mean_absolute_percentage_error within expected range below expected range above expected range
12 7.041701 80.392157 19.607843 NaN
11 6.797047 76.595745 19.148936 4.255319
10 6.937111 72.093023 20.930233 6.976744
9 7.513754 65.789474 15.789474 18.421053
8 7.252462 61.764706 23.529412 14.705882
7 6.538389 60.000000 10.000000 30.000000
6 7.678699 56.000000 16.000000 28.000000
5 6.080528 66.666667 14.285714 19.047619
4 6.382997 82.352941 17.647059 NaN
3 8.240523 75.000000 25.000000 NaN
2 8.196412 75.000000 25.000000 NaN

Creating Custom Models for Smaller Geographies¶

Now, lets retrieve the best hyperparameters for each model at borough level.

In [87]:
df.loc[:,'borough'].value_counts()
Out[87]:
borough
BROOKLYN         248046
BRONX            187793
MANHATTAN        174421
QUEENS           110118
STATEN ISLAND     22886
Unspecified        1057
Name: count, dtype: int64
In [88]:
def get_best_models_by(aggregation_level, df, all_params, level, n_months_to_predict):
    '''
    Repeats the grid search for all unique values in a certain geography or other
    aggregation level, returning the best params for each aggregation level.
    
    Inputs:
        aggregation_level: string, intended to be a column name of geographies but can
            be more flexible if needed. Examples are: `borough`, `community_board`, and
            `rat_mitigation_zone`.     
        df: pandas dataframe (before spliting for train, test - all data of interest)
        all params: list of dictionaries that have all possible options of params to try
        level: string, either 'date', 'week', or 'month'
        return_best_model_only: boolean, True if you want only the best params available, 
            False if you want results for all the models generated
        n_months_to_predict: integer for the number of months of data you want to predict
    
    Returns: dictionary of the best params for each aggregation level and for the aggregate 
    '''
    parameters_by_geog = {}
    
    unique_geogs = pd.Series(df.loc[:,aggregation_level].unique())
    unique_geogs = unique_geogs[unique_geogs.notnull()]

    for geog, n in df.loc[:,aggregation_level].value_counts().to_dict().items():
        
        #ignore certain geography types
        if 'Unspecified' in geog or 'nan' in geog:
            continue

        #ignore CBs with too little data
        if n < 100:
            continue

        print("retrieiving best model for ", geog, "...")

        # subset df by area of interest
        df_subset = df.loc[df.loc[:,aggregation_level] == geog,:]
        best_model = grid_search(df=df_subset, 
                                 all_params=all_params, 
                                 level=level, 
                                 return_best_model_only=True,
                                 n_months_to_predict=n_months_to_predict)

        print("found best model for ", geog, ".")

        parameters_by_geog[geog] = best_model
    
    return parameters_by_geog
In [89]:
borough_params = get_best_models_by(aggregation_level='borough', 
                                    df=df, 
                                    all_params=all_params, 
                                    level='week',
                                    n_months_to_predict=3)
retrieiving best model for  BROOKLYN ...
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found best model for  BROOKLYN .
retrieiving best model for  BRONX ...
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found best model for  BRONX .
retrieiving best model for  MANHATTAN ...
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found best model for  MANHATTAN .
retrieiving best model for  QUEENS ...
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found best model for  QUEENS .
retrieiving best model for  STATEN ISLAND ...
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found best model for  STATEN ISLAND .
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The "best" weekly borough models vary in parameters, so it is important to use the grid_search method in order to find the best model for each geographic subset.

In [90]:
# borough_params

Now we can do the same thing at the community_board level.

In [91]:
community_board_params = get_best_models_by(aggregation_level='community_board', 
                                            df=df, 
                                            all_params=all_params, 
                                            level='week',
                                            n_months_to_predict=3)
retrieiving best model for  04 BRONX ...
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found best model for  04 BRONX .
retrieiving best model for  12 MANHATTAN ...
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found best model for  12 MANHATTAN .
retrieiving best model for  03 BROOKLYN ...
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found best model for  03 BROOKLYN .
retrieiving best model for  10 MANHATTAN ...
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found best model for  10 MANHATTAN .
retrieiving best model for  05 BRONX ...
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found best model for  05 BRONX .
retrieiving best model for  07 BRONX ...
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found best model for  07 BRONX .
retrieiving best model for  05 BROOKLYN ...
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found best model for  05 BROOKLYN .
retrieiving best model for  17 BROOKLYN ...
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found best model for  17 BROOKLYN .
retrieiving best model for  07 MANHATTAN ...
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found best model for  07 MANHATTAN .
retrieiving best model for  14 BROOKLYN ...
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found best model for  14 BROOKLYN .
retrieiving best model for  08 BROOKLYN ...
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found best model for  08 BROOKLYN .
retrieiving best model for  12 BRONX ...
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found best model for  12 BRONX .
retrieiving best model for  04 BROOKLYN ...
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found best model for  04 BROOKLYN .
retrieiving best model for  06 BRONX ...
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found best model for  06 BRONX .
retrieiving best model for  09 BROOKLYN ...
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found best model for  09 BROOKLYN .
retrieiving best model for  09 MANHATTAN ...
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found best model for  09 MANHATTAN .
retrieiving best model for  09 BRONX ...
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found best model for  09 BRONX .
retrieiving best model for  01 BROOKLYN ...
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found best model for  01 BROOKLYN .
retrieiving best model for  11 MANHATTAN ...
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found best model for  11 MANHATTAN .
retrieiving best model for  03 MANHATTAN ...
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found best model for  03 MANHATTAN .
retrieiving best model for  12 QUEENS ...
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found best model for  12 QUEENS .
retrieiving best model for  01 STATEN ISLAND ...
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found best model for  01 STATEN ISLAND .
retrieiving best model for  03 BRONX ...
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found best model for  03 BRONX .
retrieiving best model for  08 MANHATTAN ...
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found best model for  08 MANHATTAN .
retrieiving best model for  01 QUEENS ...
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found best model for  01 QUEENS .
retrieiving best model for  01 BRONX ...
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found best model for  01 BRONX .
retrieiving best model for  05 QUEENS ...
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found best model for  05 QUEENS .
retrieiving best model for  16 BROOKLYN ...
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found best model for  16 BROOKLYN .
retrieiving best model for  11 BRONX ...
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found best model for  11 BRONX .
retrieiving best model for  02 BROOKLYN ...
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found best model for  02 BROOKLYN .
retrieiving best model for  04 MANHATTAN ...
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found best model for  04 MANHATTAN .
retrieiving best model for  02 BRONX ...
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found best model for  02 BRONX .
retrieiving best model for  06 BROOKLYN ...
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found best model for  06 BROOKLYN .
retrieiving best model for  08 BRONX ...
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found best model for  08 BRONX .
retrieiving best model for  02 MANHATTAN ...
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found best model for  02 MANHATTAN .
retrieiving best model for  11 BROOKLYN ...
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found best model for  11 BROOKLYN .
retrieiving best model for  14 QUEENS ...
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found best model for  14 QUEENS .
retrieiving best model for  07 BROOKLYN ...
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found best model for  07 BROOKLYN .
retrieiving best model for  07 QUEENS ...
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found best model for  07 QUEENS .
retrieiving best model for  12 BROOKLYN ...
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found best model for  12 BROOKLYN .
retrieiving best model for  02 QUEENS ...
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found best model for  02 QUEENS .
retrieiving best model for  09 QUEENS ...
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found best model for  09 QUEENS .
retrieiving best model for  18 BROOKLYN ...
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found best model for  18 BROOKLYN .
retrieiving best model for  04 QUEENS ...
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found best model for  04 QUEENS .
retrieiving best model for  03 QUEENS ...
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found best model for  03 QUEENS .
retrieiving best model for  15 BROOKLYN ...
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found best model for  15 BROOKLYN .
retrieiving best model for  10 BROOKLYN ...
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found best model for  10 BROOKLYN .
retrieiving best model for  06 MANHATTAN ...
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found best model for  06 MANHATTAN .
retrieiving best model for  13 BROOKLYN ...
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found best model for  13 BROOKLYN .
retrieiving best model for  10 QUEENS ...
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found best model for  10 QUEENS .
retrieiving best model for  05 MANHATTAN ...
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found best model for  05 MANHATTAN .
retrieiving best model for  08 QUEENS ...
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found best model for  08 QUEENS .
retrieiving best model for  13 QUEENS ...
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found best model for  13 QUEENS .
retrieiving best model for  10 BRONX ...
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found best model for  10 BRONX .
retrieiving best model for  06 QUEENS ...
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found best model for  06 QUEENS .
retrieiving best model for  03 STATEN ISLAND ...
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found best model for  03 STATEN ISLAND .
retrieiving best model for  02 STATEN ISLAND ...
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found best model for  02 STATEN ISLAND .
retrieiving best model for  01 MANHATTAN ...
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found best model for  01 MANHATTAN .
retrieiving best model for  11 QUEENS ...
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found best model for  11 QUEENS .
retrieiving best model for  64 MANHATTAN ...
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found best model for  64 MANHATTAN .
retrieiving best model for  55 BROOKLYN ...
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found best model for  55 BROOKLYN .
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In [92]:
community_board_params
Out[92]:
{'04 BRONX': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 6
 y_fourier                                12
 mean_absolute_percentage_error    16.840382
 within expected range                  75.0
 above expected range                   25.0
 below expected range                    NaN
 Name: 135, dtype: object,
 '12 MANHATTAN': changepoint_range                       0.8
 changepoint_prior_scale                 0.5
 m_fourier                             False
 q_fourier                                 6
 y_fourier                             False
 mean_absolute_percentage_error    19.549752
 within expected range             66.666667
 below expected range              33.333333
 Name: 12, dtype: object,
 '03 BROOKLYN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                                 4
 y_fourier                                11
 mean_absolute_percentage_error    17.552248
 within expected range             91.666667
 above expected range                    NaN
 below expected range               8.333333
 Name: 166, dtype: object,
 '10 MANHATTAN': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 7
 y_fourier                                11
 mean_absolute_percentage_error    32.639267
 below expected range              58.333333
 within expected range             41.666667
 Name: 498, dtype: object,
 '05 BRONX': changepoint_range                      0.8
 changepoint_prior_scale                0.6
 m_fourier                            False
 q_fourier                                7
 y_fourier                               11
 mean_absolute_percentage_error    13.76752
 within expected range                100.0
 below expected range                   NaN
 Name: 78, dtype: object,
 '07 BRONX': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                             False
 y_fourier                             False
 mean_absolute_percentage_error    16.210027
 within expected range             66.666667
 above expected range              16.666667
 below expected range              16.666667
 Name: 340, dtype: object,
 '05 BROOKLYN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 6
 y_fourier                             False
 mean_absolute_percentage_error    17.370425
 within expected range             91.666667
 above expected range                    NaN
 below expected range               8.333333
 Name: 132, dtype: object,
 '17 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.5
 m_fourier                             False
 q_fourier                                 6
 y_fourier                                11
 mean_absolute_percentage_error    18.616888
 within expected range                  75.0
 above expected range              16.666667
 below expected range               8.333333
 Name: 374, dtype: object,
 '07 MANHATTAN': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 4
 y_fourier                             False
 mean_absolute_percentage_error    13.109665
 within expected range             91.666667
 below expected range               8.333333
 above expected range                    NaN
 Name: 304, dtype: object,
 '14 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                                 2
 q_fourier                                 5
 y_fourier                                12
 mean_absolute_percentage_error    29.754287
 below expected range              41.666667
 within expected range             58.333333
 Name: 511, dtype: object,
 '08 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.6
 m_fourier                                 3
 q_fourier                             False
 y_fourier                                10
 mean_absolute_percentage_error    20.605508
 within expected range                  75.0
 below expected range              16.666667
 above expected range               8.333333
 Name: 461, dtype: object,
 '12 BRONX': changepoint_range                       0.8
 changepoint_prior_scale                 0.5
 m_fourier                                 2
 q_fourier                                 4
 y_fourier                             False
 mean_absolute_percentage_error    18.752258
 within expected range             66.666667
 above expected range              33.333333
 Name: 24, dtype: object,
 '04 BROOKLYN': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                             False
 y_fourier                                11
 mean_absolute_percentage_error    13.047366
 within expected range                 100.0
 above expected range                    NaN
 below expected range                    NaN
 Name: 302, dtype: object,
 '06 BRONX': changepoint_range                       0.8
 changepoint_prior_scale                 0.5
 m_fourier                             False
 q_fourier                             False
 y_fourier                             False
 mean_absolute_percentage_error     25.79457
 within expected range             66.666667
 below expected range                   25.0
 above expected range               8.333333
 Name: 0, dtype: object,
 '09 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                                 2
 q_fourier                                 6
 y_fourier                             False
 mean_absolute_percentage_error    17.330494
 within expected range                  75.0
 above expected range                   25.0
 Name: 512, dtype: object,
 '09 MANHATTAN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 7
 y_fourier                             False
 mean_absolute_percentage_error    14.210278
 within expected range                  75.0
 above expected range                   25.0
 below expected range                    NaN
 Name: 136, dtype: object,
 '09 BRONX': changepoint_range                      0.85
 changepoint_prior_scale                 0.5
 m_fourier                                 2
 q_fourier                             False
 y_fourier                                12
 mean_absolute_percentage_error    38.599037
 within expected range                  50.0
 below expected range              41.666667
 above expected range               8.333333
 Name: 203, dtype: object,
 '01 BROOKLYN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 6
 y_fourier                                12
 mean_absolute_percentage_error    69.136627
 below expected range              83.333333
 within expected range             16.666667
 Name: 135, dtype: object,
 '11 MANHATTAN': changepoint_range                      0.85
 changepoint_prior_scale                 0.5
 m_fourier                                 3
 q_fourier                                 7
 y_fourier                             False
 mean_absolute_percentage_error    10.681474
 within expected range                  75.0
 above expected range              16.666667
 below expected range               8.333333
 Name: 236, dtype: object,
 '03 MANHATTAN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 5
 y_fourier                                12
 mean_absolute_percentage_error    18.117501
 within expected range             91.666667
 below expected range               8.333333
 Name: 131, dtype: object,
 '12 QUEENS': changepoint_range                       0.9
 changepoint_prior_scale                 0.6
 m_fourier                                 3
 q_fourier                                 6
 y_fourier                                12
 mean_absolute_percentage_error     19.56006
 within expected range             91.666667
 below expected range               8.333333
 above expected range                    NaN
 Name: 475, dtype: object,
 '01 STATEN ISLAND': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                                 7
 y_fourier                                10
 mean_absolute_percentage_error    34.919789
 within expected range                  75.0
 below expected range              16.666667
 above expected range               8.333333
 Name: 177, dtype: object,
 '03 BRONX': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 7
 y_fourier                             False
 mean_absolute_percentage_error    15.036834
 within expected range             83.333333
 above expected range              16.666667
 below expected range                    NaN
 Name: 136, dtype: object,
 '08 MANHATTAN': changepoint_range                       0.8
 changepoint_prior_scale                 0.6
 m_fourier                                 3
 q_fourier                                 6
 y_fourier                                10
 mean_absolute_percentage_error    41.386778
 below expected range              58.333333
 within expected range             41.666667
 Name: 113, dtype: object,
 '01 QUEENS': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                                 6
 y_fourier                                11
 mean_absolute_percentage_error    44.723013
 below expected range                   50.0
 within expected range                  50.0
 Name: 534, dtype: object,
 '01 BRONX': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 4
 y_fourier                                11
 mean_absolute_percentage_error    17.093488
 within expected range             83.333333
 above expected range               8.333333
 below expected range               8.333333
 Name: 306, dtype: object,
 '05 QUEENS': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                             False
 y_fourier                                11
 mean_absolute_percentage_error    30.826284
 within expected range             83.333333
 above expected range               8.333333
 below expected range               8.333333
 Name: 162, dtype: object,
 '16 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.6
 m_fourier                                 3
 q_fourier                             False
 y_fourier                                12
 mean_absolute_percentage_error    12.424698
 within expected range             83.333333
 above expected range              16.666667
 Name: 463, dtype: object,
 '11 BRONX': changepoint_range                      0.8
 changepoint_prior_scale                0.7
 m_fourier                                3
 q_fourier                            False
 y_fourier                               11
 mean_absolute_percentage_error    30.06996
 within expected range                 75.0
 below expected range                  25.0
 Name: 162, dtype: object,
 '02 BROOKLYN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                                 2
 q_fourier                                 7
 y_fourier                                11
 mean_absolute_percentage_error    36.048147
 within expected range                  75.0
 below expected range                   25.0
 Name: 158, dtype: object,
 '04 MANHATTAN': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 4
 y_fourier                             False
 mean_absolute_percentage_error    38.822767
 below expected range              41.666667
 within expected range             58.333333
 Name: 484, dtype: object,
 '02 BRONX': changepoint_range                       0.9
 changepoint_prior_scale                 0.5
 m_fourier                             False
 q_fourier                             False
 y_fourier                                10
 mean_absolute_percentage_error    19.709682
 within expected range             83.333333
 above expected range               8.333333
 below expected range               8.333333
 Name: 361, dtype: object,
 '06 BROOKLYN': changepoint_range                      0.85
 changepoint_prior_scale                 0.5
 m_fourier                                 2
 q_fourier                             False
 y_fourier                                11
 mean_absolute_percentage_error    20.507614
 within expected range             83.333333
 above expected range              16.666667
 below expected range                    NaN
 Name: 202, dtype: object,
 '08 BRONX': changepoint_range                       0.8
 changepoint_prior_scale                 0.5
 m_fourier                                 3
 q_fourier                                 5
 y_fourier                                11
 mean_absolute_percentage_error    30.826841
 within expected range                  75.0
 above expected range              16.666667
 below expected range               8.333333
 Name: 50, dtype: object,
 '02 MANHATTAN': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 6
 y_fourier                                12
 mean_absolute_percentage_error    75.704042
 below expected range                   75.0
 above expected range               8.333333
 within expected range             16.666667
 Name: 495, dtype: object,
 '11 BROOKLYN': changepoint_range                       0.8
 changepoint_prior_scale                 0.6
 m_fourier                                 3
 q_fourier                                 7
 y_fourier                                11
 mean_absolute_percentage_error     22.23418
 within expected range             91.666667
 above expected range               8.333333
 below expected range                    NaN
 Name: 118, dtype: object,
 '14 QUEENS': changepoint_range                       0.8
 changepoint_prior_scale                 0.5
 m_fourier                             False
 q_fourier                             False
 y_fourier                                11
 mean_absolute_percentage_error    49.624693
 below expected range              41.666667
 within expected range                  50.0
 above expected range               8.333333
 Name: 2, dtype: object,
 '07 BROOKLYN': changepoint_range                       0.8
 changepoint_prior_scale                 0.6
 m_fourier                             False
 q_fourier                             False
 y_fourier                             False
 mean_absolute_percentage_error    29.195035
 within expected range             66.666667
 above expected range              16.666667
 below expected range              16.666667
 Name: 60, dtype: object,
 '07 QUEENS': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                                 2
 q_fourier                                 5
 y_fourier                             False
 mean_absolute_percentage_error      44.9876
 below expected range              41.666667
 within expected range             58.333333
 Name: 508, dtype: object,
 '12 BROOKLYN': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                                 6
 y_fourier                                12
 mean_absolute_percentage_error    31.538329
 within expected range             66.666667
 below expected range                   25.0
 above expected range               8.333333
 Name: 355, dtype: object,
 '02 QUEENS': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                             False
 y_fourier                                12
 mean_absolute_percentage_error    15.728034
 within expected range             83.333333
 above expected range              16.666667
 below expected range                    NaN
 Name: 163, dtype: object,
 '09 QUEENS': changepoint_range                       0.8
 changepoint_prior_scale                 0.5
 m_fourier                                 2
 q_fourier                                 6
 y_fourier                                11
 mean_absolute_percentage_error    25.034045
 within expected range                 100.0
 below expected range                    NaN
 above expected range                    NaN
 Name: 34, dtype: object,
 '18 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                             False
 y_fourier                                11
 mean_absolute_percentage_error    24.243215
 within expected range             83.333333
 above expected range               8.333333
 below expected range               8.333333
 Name: 482, dtype: object,
 '04 QUEENS': changepoint_range                       0.9
 changepoint_prior_scale                 0.5
 m_fourier                             False
 q_fourier                                 6
 y_fourier                             False
 mean_absolute_percentage_error    19.342428
 within expected range             83.333333
 below expected range               8.333333
 above expected range               8.333333
 Name: 372, dtype: object,
 '03 QUEENS': changepoint_range                       0.8
 changepoint_prior_scale                 0.5
 m_fourier                                 2
 q_fourier                                 7
 y_fourier                             False
 mean_absolute_percentage_error    34.770444
 within expected range             58.333333
 below expected range                   25.0
 above expected range              16.666667
 Name: 36, dtype: object,
 '15 BROOKLYN': changepoint_range                      0.85
 changepoint_prior_scale                 0.5
 m_fourier                                 2
 q_fourier                                 4
 y_fourier                                11
 mean_absolute_percentage_error    12.015128
 within expected range                 100.0
 Name: 206, dtype: object,
 '10 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.5
 m_fourier                                 3
 q_fourier                                 5
 y_fourier                                10
 mean_absolute_percentage_error    31.482097
 within expected range                  75.0
 below expected range              16.666667
 above expected range               8.333333
 Name: 409, dtype: object,
 '06 MANHATTAN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 4
 y_fourier                                12
 mean_absolute_percentage_error    68.428587
 within expected range             58.333333
 below expected range              41.666667
 Name: 127, dtype: object,
 '13 BROOKLYN': changepoint_range                       0.85
 changepoint_prior_scale                  0.7
 m_fourier                              False
 q_fourier                              False
 y_fourier                                 11
 mean_absolute_percentage_error    107.368883
 below expected range               58.333333
 within expected range              41.666667
 Name: 302, dtype: object,
 '10 QUEENS': changepoint_range                       0.8
 changepoint_prior_scale                 0.6
 m_fourier                             False
 q_fourier                                 6
 y_fourier                                12
 mean_absolute_percentage_error    26.343264
 within expected range                 100.0
 below expected range                    NaN
 Name: 75, dtype: object,
 '05 MANHATTAN': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                                 2
 q_fourier                             False
 y_fourier                                12
 mean_absolute_percentage_error    93.741929
 within expected range             58.333333
 below expected range              41.666667
 Name: 323, dtype: object,
 '08 QUEENS': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                                 2
 q_fourier                             False
 y_fourier                                12
 mean_absolute_percentage_error    47.172865
 within expected range             84.615385
 below expected range              15.384615
 Name: 323, dtype: object,
 '13 QUEENS': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                             False
 y_fourier                             False
 mean_absolute_percentage_error    20.636491
 within expected range             92.307692
 above expected range               7.692308
 Name: 300, dtype: object,
 '10 BRONX': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                                 6
 y_fourier                                11
 mean_absolute_percentage_error    57.760585
 below expected range              16.666667
 within expected range             83.333333
 Name: 534, dtype: object,
 '06 QUEENS': changepoint_range                      0.85
 changepoint_prior_scale                 0.6
 m_fourier                                 3
 q_fourier                                 5
 y_fourier                             False
 mean_absolute_percentage_error    75.169459
 below expected range              41.666667
 within expected range             58.333333
 Name: 288, dtype: object,
 '03 STATEN ISLAND': changepoint_range                      0.85
 changepoint_prior_scale                 0.7
 m_fourier                                 3
 q_fourier                                 4
 y_fourier                             False
 mean_absolute_percentage_error     43.65174
 within expected range             83.333333
 below expected range               8.333333
 above expected range               8.333333
 Name: 344, dtype: object,
 '02 STATEN ISLAND': changepoint_range                        0.9
 changepoint_prior_scale                  0.6
 m_fourier                              False
 q_fourier                                  7
 y_fourier                                 10
 mean_absolute_percentage_error    128.524275
 within expected range              81.818182
 below expected range                9.090909
 above expected range                9.090909
 Name: 437, dtype: object,
 '01 MANHATTAN': changepoint_range                       0.8
 changepoint_prior_scale                 0.7
 m_fourier                                 2
 q_fourier                                 7
 y_fourier                                11
 mean_absolute_percentage_error    42.059296
 within expected range             92.307692
 below expected range               7.692308
 Name: 158, dtype: object,
 '11 QUEENS': changepoint_range                        0.8
 changepoint_prior_scale                  0.5
 m_fourier                              False
 q_fourier                                  6
 y_fourier                                 12
 mean_absolute_percentage_error    112.830175
 below expected range               41.666667
 within expected range              58.333333
 Name: 15, dtype: object,
 '64 MANHATTAN': changepoint_range                       0.85
 changepoint_prior_scale                  0.5
 m_fourier                                  3
 q_fourier                              False
 y_fourier                              False
 mean_absolute_percentage_error    234.843229
 below expected range               28.571429
 within expected range              71.428571
 Name: 220, dtype: object,
 '55 BROOKLYN': changepoint_range                       0.9
 changepoint_prior_scale                 0.7
 m_fourier                             False
 q_fourier                                 5
 y_fourier                                11
 mean_absolute_percentage_error    45.666845
 above expected range                   25.0
 within expected range                  62.5
 below expected range                   12.5
 Name: 490, dtype: object}
In [108]:
(pd.DataFrame(community_board_params).T.mean_absolute_percentage_error).mean()
Out[108]:
38.58587571752581

Create new df that subsets to only requests in RMZs. Then create estimates at that level as well.

In [93]:
# #subset df to only RMZs
# df_only_rmzs = df.loc[df.loc[:,'is_rmz'].notna(),:]

# best_all_rmz_model = grid_search(df=df_only_rmzs, 
#                                 all_params=all_params,
#                                 level='week', 
#                                 return_best_model_only=True,
#                                 n_months_to_predict=3)
In [94]:
# rat_mitigation_zone_params = get_best_models_by(aggregation_level='rat_mitigation_zone', 
#                                             df=df_only_rmzs, 
#                                             all_params=all_params, 
#                                             level='week',
#                                             n_months_to_predict=3)
In [95]:
# rat_mitigation_zone_params

Data Export for PowerBI¶

Now that we're all set up with the best models for each geography, let's package the data to use in the PowerBI dashboard.

In [96]:
from datetime import date

def save_as_csv(parameters_by_geog,
               parameters_citywide,
               aggregation_level, 
               df,
               level,
               n_months_to_predict=3):
    '''
    Use the best params for each aggregation level to make predictions and then save the data accordingly.
    
    Inputs:
        parameters_by_geog: dictionary, key is a string of the unit of geography, value is a dictionary with
            the best parameters to use for that unit of geography
        parameters_citywide: dictionary, key is the string name of the param, value is a string of the param
        aggregation_level: string, intended to be a column name of geographies but can
            be more flexible if needed. Examples are: `borough`, `community_board`, and
            `rat_mitigation_zone`.     
        df: pandas dataframe (before spliting for train, test - all data of interest)
        level: string, either 'date', 'week', or 'month'
        n_months_to_predict: integer for the number of months of data you want to predict
    
    Returns: combined pandas dataframe of all predicted values, with 'geography' as the column that distinguishes
        between the predictions of each type. Saves the dataframe as a csv to a folder called 'history', 
        with the filepath as the name of the aggregation level and the date of the run 
        (e.g. 'borough_predictions_2023-08-08.csv').
    '''
    
    df_list = []

    # get city-wide predictions
    city_df = get_aggregates(df=df, level=level)

    train, test = train_test_split(df=city_df, 
                                   n_months_to_predict=n_months_to_predict)
    
    m = build_model(parameters_citywide)

    forecast = get_forecast(model=m, 
                        train=train, 
                        test=test, 
                        level=level,
                        plot=False,
                        title_suffix='All NYC')
    
    #couple extra columns for PowerBI
    forecast.loc[:,'in_conf_int'] = "within expected range"
    forecast.loc[(forecast.loc[:,'y'] > forecast.loc[:,'yhat_upper']), 'in_conf_int'] = "above expected range"
    forecast.loc[(forecast.loc[:,'y'] < forecast.loc[:,'yhat_lower']), 'in_conf_int'] = "below expected range"
    forecast['difference'] = forecast['y'] - forecast['yhat']

    #numeric column
    forecast.loc[:,'in_conf_int_numeric'] = 1
    forecast.loc[(forecast.loc[:,'y'] > forecast.loc[:,'yhat_upper']), 'in_conf_int_numeric'] = 2
    forecast.loc[(forecast.loc[:,'y'] < forecast.loc[:,'yhat_lower']), 'in_conf_int_numeric'] = 0
    
    full_df = pd.concat([train.loc[:,['ds','y']], forecast], axis=0)
    
    if aggregation_level == 'rat_mitigation_zone':
        full_df.loc[:, 'geography'] = 'ALL RMZs'
    else:
        full_df.loc[:, 'geography'] = 'ALL NYC'

    df_list.append(full_df)

    # get predictions at aggregation level
    for geog, params in parameters_by_geog.items():

        df_subset = df.loc[df.loc[:,aggregation_level] == geog,:]
        
        aggregated_df = get_aggregates(df=df_subset, level=level)
        
        # use function to get training and test data sets
        train, test = train_test_split(df=aggregated_df, 
                                       n_months_to_predict=n_months_to_predict)

        # set model with passed in parameters
        m = build_model(params)
        
        # get forecast
        forecast = get_forecast(model=m, 
                                train=train, 
                                test=test, 
                                level=level,
                                plot=False,
                                title_suffix=geog)
        
        #couple extra columns for PowerBI
        forecast.loc[:,'in_conf_int'] = "within expected range"
        forecast.loc[(forecast.loc[:,'y'] > forecast.loc[:,'yhat_upper']), 'in_conf_int'] = "above expected range"
        forecast.loc[(forecast.loc[:,'y'] < forecast.loc[:,'yhat_lower']), 'in_conf_int'] = "below expected range"
        forecast['difference'] = forecast['y'] - forecast['yhat']

        #numeric column
        forecast.loc[:,'in_conf_int_numeric'] = 1
        forecast.loc[(forecast.loc[:,'y'] > forecast.loc[:,'yhat_upper']), 'in_conf_int_numeric'] = 2
        forecast.loc[(forecast.loc[:,'y'] < forecast.loc[:,'yhat_lower']), 'in_conf_int_numeric'] = 0
        
        full_df = pd.concat([train.loc[:,['ds','y']], forecast], axis=0)
        full_df.loc[:, 'geography'] = geog #.upper()

        df_list.append(full_df)
        
    combined_df = pd.concat(df_list, axis=0)
    combined_df['ds'] = combined_df['ds'].apply(lambda x: x.round('D'))
    
    #save locally
    filepath_history = 'history/'+ aggregation_level + '_predictions_' + str(date.today()) + '.csv'
    combined_df.to_csv(filepath_history)
    
    return combined_df

Use the above function to generate predictions at three different levels of geography.

In [97]:
# borough_predictions = save_as_csv(parameters_by_geog=borough_params,
#                                  parameters_citywide=best_city_model,
#                                  aggregation_level='borough',
#                                  df=df,
#                                  level='week',
#                                  n_months_to_predict=3)
In [98]:
# borough_predictions
In [99]:
community_board_predictions = save_as_csv(parameters_by_geog=community_board_params,
                                         parameters_citywide=best_city_model,
                                         aggregation_level='community_board',
                                         df=df,
                                         level='week',
                                         n_months_to_predict=3)
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ih1tp05q.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/f9pn17kq.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=81225', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ih1tp05q.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/f9pn17kq.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelhjv27qga/prophet_model-20240112174355.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:43:55 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:43:56 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/4uunm3kf.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/b1m_jbur.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=56302', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/4uunm3kf.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/b1m_jbur.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeld92pw1bq/prophet_model-20240112174358.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:43:58 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:43:58 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/3m6xqs38.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/82bbv5_8.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=38381', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/3m6xqs38.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/82bbv5_8.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelji_zo5ri/prophet_model-20240112174359.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:43:59 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:00 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/pxucpugh.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/p5w9sdci.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=66825', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/pxucpugh.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/p5w9sdci.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelr_t9yv9q/prophet_model-20240112174401.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:01 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:01 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/w68_e_jm.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/0cs07w98.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=32408', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/w68_e_jm.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/0cs07w98.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model1e7uovi_/prophet_model-20240112174403.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:03 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:03 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_7w4jhbf.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/mgkxatw6.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=87777', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_7w4jhbf.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/mgkxatw6.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelo4i34a53/prophet_model-20240112174404.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:04 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:05 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/zuw6c48h.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/tw5_hqee.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=40925', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/zuw6c48h.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/tw5_hqee.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeleud74akn/prophet_model-20240112174406.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:06 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:06 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/82vscxm5.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/bj9k2dqo.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=202', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/82vscxm5.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/bj9k2dqo.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelivo0vodp/prophet_model-20240112174407.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:07 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:08 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/od8jy8ty.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/u6c1xinr.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=34635', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/od8jy8ty.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/u6c1xinr.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model4t0aj9r_/prophet_model-20240112174409.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:09 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:10 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ls5qu3un.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/15na3jhf.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=63694', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ls5qu3un.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/15na3jhf.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelicvau6we/prophet_model-20240112174411.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:11 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:11 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6o2__vqt.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/nn42eg4f.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=47568', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6o2__vqt.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/nn42eg4f.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeli82nowoo/prophet_model-20240112174412.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:12 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:13 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/mt6ylh70.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ccybnvbt.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=62917', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/mt6ylh70.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ccybnvbt.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelxcam2f1u/prophet_model-20240112174414.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:14 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:14 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/cm6ky_y2.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/at02v9g9.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=5399', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/cm6ky_y2.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/at02v9g9.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model0z8urnj9/prophet_model-20240112174416.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:16 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:16 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/xe1esofd.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/fik8_k78.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=76080', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/xe1esofd.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/fik8_k78.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model__ecdk_v/prophet_model-20240112174417.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:17 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:18 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/b8csb788.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ccmz6o8_.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=90464', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/b8csb788.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ccmz6o8_.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelegx6qb_t/prophet_model-20240112174419.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:19 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:19 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ia9tbz02.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y15_g2hq.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=66156', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ia9tbz02.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y15_g2hq.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeljko5u2lz/prophet_model-20240112174420.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:20 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:21 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ir4x2azo.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/rwbn2_1o.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=25931', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ir4x2azo.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/rwbn2_1o.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelmla_3ho_/prophet_model-20240112174422.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:22 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:22 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/vewb3ubl.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/hodququ4.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=22262', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/vewb3ubl.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/hodququ4.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelu8kchlhf/prophet_model-20240112174423.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:23 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:24 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_997l2h_.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/85kkc6mr.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=32908', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_997l2h_.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/85kkc6mr.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeld3nfhfd4/prophet_model-20240112174425.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:25 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:25 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1ik53sbk.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/3qi12bdg.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=3645', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1ik53sbk.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/3qi12bdg.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelvrlgn6_c/prophet_model-20240112174427.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:27 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:27 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/rv_armlw.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6kktk9wk.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=3326', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/rv_armlw.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6kktk9wk.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model37lctbi0/prophet_model-20240112174429.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:29 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:29 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/d1u_byn_.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/iggfwxw0.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=45560', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/d1u_byn_.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/iggfwxw0.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelgw4dly51/prophet_model-20240112174432.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:32 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:32 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/2kxeqpu4.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/m5wk96mz.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=67008', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/2kxeqpu4.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/m5wk96mz.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model5m1it3ik/prophet_model-20240112174435.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:35 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:35 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6a_skzpv.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/0czwv7dz.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=57268', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6a_skzpv.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/0czwv7dz.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelwau2lgbg/prophet_model-20240112174437.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:37 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:38 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1u67kps3.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y70wjmso.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=62943', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1u67kps3.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y70wjmso.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modela5_q0vdg/prophet_model-20240112174439.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:39 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:39 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/pf9on6yq.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/l7nforn8.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=1559', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/pf9on6yq.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/l7nforn8.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelbn__zpqx/prophet_model-20240112174440.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:40 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:41 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/53phlzhs.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5qn6rzf6.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=52936', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/53phlzhs.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5qn6rzf6.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeldi6gk40o/prophet_model-20240112174442.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:42 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:42 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5i0ghbry.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/yuv9y37g.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=32860', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5i0ghbry.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/yuv9y37g.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model263nx6_p/prophet_model-20240112174444.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:44 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:44 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gpg4wzxo.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/qbgx4jjz.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=29063', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gpg4wzxo.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/qbgx4jjz.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelrxforoj3/prophet_model-20240112174445.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:45 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:45 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y4w3xr85.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_7oil_br.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=1403', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y4w3xr85.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_7oil_br.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelspz9o_hv/prophet_model-20240112174446.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:46 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:47 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/a87808_o.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ken6918_.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=4125', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/a87808_o.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ken6918_.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelwykhrfqq/prophet_model-20240112174448.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:48 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:48 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/oki3wxz9.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6uictrq6.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=36337', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/oki3wxz9.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6uictrq6.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelmo7f707g/prophet_model-20240112174449.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:49 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:49 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/9lgyzupr.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/hnl1wykw.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=43802', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/9lgyzupr.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/hnl1wykw.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelv9g8x4xf/prophet_model-20240112174450.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:50 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:51 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/jhzwjup5.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/m1jvq3hs.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=55127', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/jhzwjup5.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/m1jvq3hs.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelj63m0a2x/prophet_model-20240112174452.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:52 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:52 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/12p3zy1k.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gehi2sre.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=48334', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/12p3zy1k.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gehi2sre.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelbqomu7er/prophet_model-20240112174453.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:53 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:54 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1_fcm5_f.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/f240yrds.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=3835', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1_fcm5_f.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/f240yrds.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelptr37c71/prophet_model-20240112174455.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:55 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:55 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/4x0t816e.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/g9upl2oi.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=89280', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/4x0t816e.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/g9upl2oi.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelx5artyjd/prophet_model-20240112174456.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:56 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:57 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6j5hc277.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/8yht0vws.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=47063', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6j5hc277.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/8yht0vws.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelouz2havm/prophet_model-20240112174458.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:58 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:58 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/oovyz76n.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/hch93l8h.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=64577', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/oovyz76n.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/hch93l8h.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelltinbi4y/prophet_model-20240112174459.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:44:59 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:44:59 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gjz81oym.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/iy4b5i2r.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=32756', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gjz81oym.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/iy4b5i2r.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelyr46uglg/prophet_model-20240112174501.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:01 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:01 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/23m_nk2y.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/pxaojspv.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=82491', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/23m_nk2y.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/pxaojspv.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model8_s2c0ns/prophet_model-20240112174502.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:02 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:02 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/2bvgf5b9.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ozqqcgrk.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=99705', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/2bvgf5b9.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ozqqcgrk.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelfjnh8yuw/prophet_model-20240112174503.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:03 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:04 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ekwwh4yq.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/n3xxua6i.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=34970', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ekwwh4yq.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/n3xxua6i.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model9sl33ays/prophet_model-20240112174505.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:05 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:05 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5agmx_lj.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/m4rhff_h.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=64325', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5agmx_lj.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/m4rhff_h.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model3p_5qjak/prophet_model-20240112174506.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:06 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:06 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/r21nlh8u.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/awt6fkch.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=12133', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/r21nlh8u.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/awt6fkch.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelidibxyal/prophet_model-20240112174507.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:07 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:08 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/i2manigu.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/4ch25z9t.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=94696', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/i2manigu.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/4ch25z9t.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeleb3930o2/prophet_model-20240112174509.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:09 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:09 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/t4vtv_47.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/em2hcr3e.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=48958', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/t4vtv_47.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/em2hcr3e.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modellxya6taj/prophet_model-20240112174510.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:10 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:11 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/67uz3rgn.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6jxnb_gm.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=66720', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/67uz3rgn.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/6jxnb_gm.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelotgtyxs_/prophet_model-20240112174512.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:12 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:12 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/qwb6d068.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1q0997rr.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=22216', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/qwb6d068.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/1q0997rr.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model57pko96p/prophet_model-20240112174513.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:13 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:13 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/65r461eo.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/uc46mjdi.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=32978', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/65r461eo.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/uc46mjdi.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelznhms3rg/prophet_model-20240112174514.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:14 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:15 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/7th4bn8z.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/cos1h1ty.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=55612', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/7th4bn8z.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/cos1h1ty.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model0ht8b05n/prophet_model-20240112174516.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:16 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:16 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/o011152t.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/igy1qx4d.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=10476', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/o011152t.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/igy1qx4d.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeldaah0ph6/prophet_model-20240112174517.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:17 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:17 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ec_63d9x.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/w7ui2im5.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=55278', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ec_63d9x.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/w7ui2im5.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelegnr5ge_/prophet_model-20240112174518.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:18 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:19 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ith1odqq.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/e4y61yn4.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=56740', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/ith1odqq.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/e4y61yn4.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelbuippiby/prophet_model-20240112174520.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:20 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:20 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_vaz89e9.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gnfnzzhc.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=56081', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_vaz89e9.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/gnfnzzhc.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modeln10t5cei/prophet_model-20240112174521.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:21 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:21 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/039m6tca.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/65irdipb.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=14939', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/039m6tca.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/65irdipb.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelzq8miicd/prophet_model-20240112174522.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:22 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:23 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/zipf0lpp.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/v5_8jgzz.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=46062', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/zipf0lpp.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/v5_8jgzz.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model63ouio1v/prophet_model-20240112174524.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:24 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:24 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y4sc5pk3.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_1f118pi.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=78965', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/y4sc5pk3.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/_1f118pi.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_model4ir4fwpv/prophet_model-20240112174525.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:25 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:25 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/umcyxq71.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/jeta3jbi.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=62739', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/umcyxq71.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/jeta3jbi.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelkptsrw97/prophet_model-20240112174526.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:26 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:26 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/rx2hjfm1.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/qh2emufo.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=21373', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/rx2hjfm1.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/qh2emufo.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelk6xua12l/prophet_model-20240112174528.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:28 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:28 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/nnk_8kwz.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/b2vvp348.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=83761', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/nnk_8kwz.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/b2vvp348.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modelcuxtecnw/prophet_model-20240112174529.csv', 'method=optimize', 'algorithm=lbfgs', 'iter=10000']
17:45:29 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:29 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
INFO:prophet:Found custom seasonality named 'yearly', disabling built-in 'yearly' seasonality.
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/xqzzrck6.json
DEBUG:cmdstanpy:input tempfile: /var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5r8060m4.json
DEBUG:cmdstanpy:idx 0
DEBUG:cmdstanpy:running CmdStan, num_threads: None
DEBUG:cmdstanpy:CmdStan args: ['/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/prophet/stan_model/prophet_model.bin', 'random', 'seed=90438', 'data', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/xqzzrck6.json', 'init=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/5r8060m4.json', 'output', 'file=/var/folders/ht/kvffqbbs10j_zxqnj4mprjv40000gn/T/tmpld79p13h/prophet_modellpp33etv/prophet_model-20240112174530.csv', 'method=optimize', 'algorithm=newton', 'iter=10000']
17:45:30 - cmdstanpy - INFO - Chain [1] start processing
INFO:cmdstanpy:Chain [1] start processing
17:45:31 - cmdstanpy - INFO - Chain [1] done processing
INFO:cmdstanpy:Chain [1] done processing
In [100]:
community_board_predictions
Out[100]:
ds y trend yhat_lower yhat_upper trend_lower trend_upper additive_terms additive_terms_lower additive_terms_upper ... yearly_lower yearly_upper multiplicative_terms multiplicative_terms_lower multiplicative_terms_upper yhat in_conf_int difference in_conf_int_numeric geography
314 2014-06-02 1056 NaN NaN NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN ALL NYC
328 2014-06-09 1134 NaN NaN NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN ALL NYC
342 2014-06-16 1240 NaN NaN NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN ALL NYC
356 2014-06-23 1192 NaN NaN NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN ALL NYC
370 2014-06-30 1056 NaN NaN NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN ALL NYC
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
3 2023-10-15 3 0.381865 0.053569 1.560463 0.381777 0.381865 0.416409 0.416409 0.416409 ... 0.145770 0.145770 0.0 0.0 0.0 0.798274 above expected range 2.201726 2.0 55 BROOKLYN
4 2023-10-22 1 0.376645 0.263967 1.697340 0.376336 0.376708 0.623157 0.623157 0.623157 ... 0.056156 0.056156 0.0 0.0 0.0 0.999802 within expected range 0.000198 1.0 55 BROOKLYN
5 2023-10-29 2 0.371424 1.202689 2.645932 0.370857 0.371648 1.545915 1.545915 1.545915 ... 0.923949 0.923949 0.0 0.0 0.0 1.917340 within expected range 0.082660 1.0 55 BROOKLYN
6 2023-11-05 1 0.366204 1.705145 3.142135 0.365252 0.366767 2.040411 2.040411 2.040411 ... 1.564518 1.564518 0.0 0.0 0.0 2.406615 below expected range -1.406615 0.0 55 BROOKLYN
7 2023-11-12 1 0.360984 0.813457 2.304316 0.359734 0.361898 1.196835 1.196835 1.196835 ... 0.992047 0.992047 0.0 0.0 0.0 1.557819 within expected range -0.557819 1.0 55 BROOKLYN

30140 rows × 27 columns

In [ ]:
# rat_mitigation_zone_predictions = save_as_csv(parameters_by_geog=rat_mitigation_zone_params,
#                                              parameters_citywide=best_all_rmz_model,
#                                              aggregation_level='rat_mitigation_zone',
#                                              df=df_only_rmzs,
#                                              level='week',
#                                              n_months_to_predict=3)

For ease of use in PowerBI, concatentate the community board and rat mitigation zone predictions together.

In [ ]:
# #combine these into one dataframe
# cb_and_rmz_predictions = pd.concat([community_board_predictions.reset_index(), 
#                                     rat_mitigation_zone_predictions.reset_index()], axis=0).drop(columns=['index'])

# # THIS OVERRIDES THE HISTORIC VERSIONS OF THE MODEL - ONLY DO THIS WHEN YOU WANT TO RESET THE DASHBOARD DATA
# # borough_predictions.to_csv("borough_predictions.csv")
# # cb_and_rmz_predictions.drop(columns='index').to_csv("cb_and_rmz_predictions.csv")
Appending most recent weekly predictions to the end of the existing dataframes¶

In order to keep the dashboard values constant, we will only append the new model predictions to the existing csvs.

In [ ]:
# def update_dashboard_predictions(filepath, updated_predictions):
#     '''
#     Appends on the dates not already in the dashboard predictions to the csv.
    
#     Inputs:
#         filepath (str): 'borough_predictions.csv' or 'cb_and_rmz_predictions.csv'
#         updated_predictions: pandas DataFrame from the above functions
    
#     Returns: nothing. Prints an update of what action is performed, but changes the csv in place.
#     '''
    
#     dashboard_predictions = pd.read_csv(filepath)
    
#     # do not modify if there is no new data
#     if max(updated_predictions['ds']) == pd.to_datetime(max(dashboard_predictions['ds'])):
#         print(f'No new complete week predictions for {filepath} to include. No changes to csv.')
#         return
    
#     newest_rows = updated_predictions.loc[updated_predictions.loc[:,'ds'] == max(updated_predictions['ds']),:]
    
#     print(f'Appending new complete week predictions to {filepath}...')
#     updated_dashboard_predictions = pd.concat([dashboard_predictions.reset_index(), 
#                                                newest_rows.reset_index()], axis=0).drop(columns=['index','Unnamed: 0'])
    
#     #make sure all dates are in the same datetime format
#     updated_dashboard_predictions.loc[:,'ds'] = pd.to_datetime(updated_dashboard_predictions.loc[:,'ds']).dt.round('D')

#     #resave as csv, overwriting the current predictions
#     print(f'Overwriting {filepath}')
#     updated_dashboard_predictions.to_csv(filepath)
    
#     return
In [ ]:
# update_dashboard_predictions('borough_predictions.csv', borough_predictions)
# update_dashboard_predictions('cb_and_rmz_predictions.csv', cb_and_rmz_predictions)
Saving to the Sharepoint Folder¶

Now that we have the csvs we want to use for the dashboard, we need to connect to a Sharepoint Site that can store this data in order to feed into the dashboard. To connect, we need to save the following as environmental variables before proceeding: RDP_SHAREPOINT_URL, RDP_SHAREPOINT_CLIENT_ID, and RDP_SHAREPOINT_CLIENT_SECRET.

This project has these variables already saved.

Martha Norrick (current CAO) created a few custom functions to connect to a Sharepoint site through Domino and save files directly. These functions are saved in the sharepoint_helpers.py script in this directory. We can first import the functions we need to use, and then use them to save our predictions csvs accordingly.

In [ ]:
# pip install office365-REST-Python-Client
In [ ]:
# import os
# from office365.sharepoint.client_context import ClientContext
# from office365.runtime.auth.client_credential import ClientCredential

# from input.sharepoint_helpers import instatiate_sharepoint_conn, enum_folder_gen_list, append_name_to_list
# from input.sharepoint_helpers import list_sharepoint_files_in_folder, extract_files, upload_file_to_sharepoint

# os.chdir('/mnt')
# ctx = instatiate_sharepoint_conn()
# target_folder_url = "dashboards/RatStat"
In [ ]:
# upload_file_to_sharepoint(ctx, 'borough_predictions.csv', target_folder_url)
# upload_file_to_sharepoint(ctx, 'cb_and_rmz_predictions.csv', target_folder_url)

Done!